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Deck 8: Applications of Trigonometry
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Question
The volume V of the right triangular prism shown in the figure is 
where B is the area of the base and h is the height of the prism. 
Approximate h, if 
.
A)5.6
B)19.5
C)20.7
D)19.9
E)21.1
where B is the area of the base and h is the height of the prism. Approximate h, if .A)5.6
B)19.5
C)20.7
D)19.9
E)21.1
Question
Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle 
, as shown in the figure. 
If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector 
.
A)19.60
B)19.90
C)19.30
D)0
E)19.84
, as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .A)19.60
B)19.90
C)19.30
D)0
E)19.84
Question
Express in the form 
, where a and b are real numbers. 
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
Question
Represent the complex number geometrically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A straight road makes an angle of 
with the horizontal. When the angle of elevation of the sun is 
, a vertical pole at the side of the road casts a shadow 
feet long directly down the road, as shown in the figure. 
Approximate the length of the pole.
A)101.34 ft
B)99.84 ft
C)100.74 ft
D)100.44 ft
E)66.74 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)101.34 ft
B)99.84 ft
C)100.74 ft
D)100.44 ft
E)66.74 ft
Question
Express the complex number in trigonometric form with 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Express in the form 
, where a and b are real numbers. 
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
Question
A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( 
). 
A)9.80 acres
B)10.13 acres
C)10.41 acres
D)3.13 acres
E)11.00 acres
). A)9.80 acres
B)10.13 acres
C)10.41 acres
D)3.13 acres
E)11.00 acres
Question
Find (a) the dot product of the two vectors and (b) the angle between the two vectors. 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum 
If 
the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
Question
A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is 
. When it is viewed at a distance of 
feet from the base of the hill, the angle of elevation is 
. The hill rises at an angle of 
. 
Approximate the height of the cathedral.
A)737 ft
B)735 ft
C)1,610 ft
D)739 ft
E)733 ft
. When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.A)737 ft
B)735 ft
C)1,610 ft
D)739 ft
E)733 ft
Question
Question
Find 2a - 3b. a = i + 2j, b = 3i - 5j
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Represent the complex number geometrically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use trigonometric forms to find 
and 
. 
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
Question
Determine m such that the two vectors are orthogonal. 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
Find the absolute value. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A jet airplane approaches a runway at an angle of 
with the horizontal, traveling at a speed of 145 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.
A)vertical = 22.53 mi/hr, horizontal = 143.76 mi/hr
B)vertical = 143.76 mi/hr , horizontal = 143.76 mi/hr
C)vertical = 17.73 mi/hr, horizontal = 143.76 mi/hr
D)vertical = 17.73 mi/hr, horizontal = 17.73 mi/hr
E)vertical = 18.93 mi/hr, horizontal = 143.76 mi/hr
with the horizontal, traveling at a speed of 145 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.A)vertical = 22.53 mi/hr, horizontal = 143.76 mi/hr
B)vertical = 143.76 mi/hr , horizontal = 143.76 mi/hr
C)vertical = 17.73 mi/hr, horizontal = 143.76 mi/hr
D)vertical = 17.73 mi/hr, horizontal = 17.73 mi/hr
E)vertical = 18.93 mi/hr, horizontal = 143.76 mi/hr
Question
If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. 
and 
A)2
B)4
C)26
D)7
E)-14
and A)2
B)4
C)26
D)7
E)-14
Question
The volume V of the right triangular prism shown in the figure is 
where B is the area of the base and h is the height of the prism. 
Approximate h, if 
.
A)6.2
B)22.6
C)23.0
D)22.2
E)21.0
where B is the area of the base and h is the height of the prism. Approximate h, if .A)6.2
B)22.6
C)23.0
D)22.2
E)21.0
Question
Represent the complex number geometrically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A jet airplane approaches a runway at an angle of 
with the horizontal, traveling at a speed of 175 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.
A)vertical = 25.56 mi/hr, horizontal = 173.30 mi/hr
B)vertical = 173.30 mi/hr , horizontal = 173.30 mi/hr
C)vertical = 25.56 mi/hr, horizontal = 25.56 mi/hr
D)vertical = 24.36 mi/hr, horizontal = 173.30 mi/hr
E)vertical = 20.76 mi/hr, horizontal = 173.30 mi/hr
with the horizontal, traveling at a speed of 175 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.A)vertical = 25.56 mi/hr, horizontal = 173.30 mi/hr
B)vertical = 173.30 mi/hr , horizontal = 173.30 mi/hr
C)vertical = 25.56 mi/hr, horizontal = 25.56 mi/hr
D)vertical = 24.36 mi/hr, horizontal = 173.30 mi/hr
E)vertical = 20.76 mi/hr, horizontal = 173.30 mi/hr
Question
Represent the complex number geometrically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Express the complex number in trigonometric form with 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the absolute value. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find (a) the dot product of the two vectors and (b) the angle between the two vectors. 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. 
and 
A)32
B)14
C)44
D)-8
E)22
and A)32
B)14
C)44
D)-8
E)22
Question
Find the two square roots of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A straight road makes an angle of 
with the horizontal. When the angle of elevation of the sun is 
, a vertical pole at the side of the road casts a shadow 
feet long directly down the road, as shown in the figure. 
Approximate the length of the pole.
A)114.56 ft
B)113.36 ft
C)114.86 ft
D)114.26 ft
E)75.70 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)114.56 ft
B)113.36 ft
C)114.86 ft
D)114.26 ft
E)75.70 ft
Question
Question
The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine m such that the two vectors are orthogonal. 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is 
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. 
A)
B)
C)
D)
E)
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. A)
B)
C)
D)
E)
Question
Find 5a - 2b. a = i + 4j, b = 6i - 6j
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( 
). 
A)10.89 acres
B)11.17 acres
C)3.39 acres
D)11.50 acres
E)10.30 acres
). A)10.89 acres
B)11.17 acres
C)3.39 acres
D)11.50 acres
E)10.30 acres
Question
A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is 
. When it is viewed at a distance of 
feet from the base of the hill, the angle of elevation is 
. The hill rises at an angle of 
. 
Approximate the height of the cathedral.
A)605 ft
B)607 ft
C)601 ft
D)1,561 ft
E)599 ft
. When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.A)605 ft
B)607 ft
C)601 ft
D)1,561 ft
E)599 ft
Question
Find the two square roots of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle 
, as shown in the figure. 
If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector 
.
A)0
B)7.23
C)7.17
D)7.20
E)7.99
, as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .A)0
B)7.23
C)7.17
D)7.20
E)7.99
Question
If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum 
If 
the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
Question
Express in the form 
, where a and b are real numbers. 
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
Question
Express in the form 
, where a and b are real numbers. 
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
Question
The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is 
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. 
A)
B)
C)
D)
E)
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. A)
B)
C)
D)
E)
Question
Question
Find the two square roots of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use trigonometric forms to find 
and 
. 
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
Question
If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. 
and 
A)48
B)12
C)-24
D)-12
E)21
and A)48
B)12
C)-24
D)-12
E)21
Question
A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( 
). 
A)10.67 acres
B)11.00 acres
C)11.28 acres
D)3.27 acres
E)9.47 acres
). A)10.67 acres
B)11.00 acres
C)11.28 acres
D)3.27 acres
E)9.47 acres
Question
A straight road makes an angle of 
with the horizontal. When the angle of elevation of the sun is 
, a vertical pole at the side of the road casts a shadow 
feet long directly down the road, as shown in the figure. 
Approximate the length of the pole.
A)94.60 ft
B)94.90 ft
C)62.67 ft
D)94.00 ft
E)95.50 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)94.60 ft
B)94.90 ft
C)62.67 ft
D)94.00 ft
E)95.50 ft
Question
Find (a) the dot product of the two vectors and (b) the angle between the two vectors. 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is 
. When it is viewed at a distance of 
feet from the base of the hill, the angle of elevation is 
. The hill rises at an angle of 
. 
Approximate the height of the cathedral.
A)1,200 ft
B)483 ft
C)487 ft
D)489 ft
E)481 ft
. When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.A)1,200 ft
B)483 ft
C)487 ft
D)489 ft
E)481 ft
Question
The volume V of the right triangular prism shown in the figure is 
where B is the area of the base and h is the height of the prism. 
Approximate h, if 
.
A)4.9
B)18.8
C)18.4
D)18.0
E)17.6
where B is the area of the base and h is the height of the prism. Approximate h, if .A)4.9
B)18.8
C)18.4
D)18.0
E)17.6
Question
Determine m such that the two vectors are orthogonal. 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
Find the two square roots of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the absolute value. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum 
If 
the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
Question
Find 4a - 6b. a = i + 4j, b = 5i - 2j
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle 
, as shown in the figure. 
If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector 
.
A)24.74
B)26.99
C)25.50
D)26.28
E)0
, as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .A)24.74
B)26.99
C)25.50
D)26.28
E)0
Question
A jet airplane approaches a runway at an angle of 
with the horizontal, traveling at a speed of 165 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.
A)vertical = 21.76 mi/hr, horizontal = 163.39 mi/hr
B)vertical = 163.39 mi/hr , horizontal = 163.39 mi/hr
C)vertical = 22.96 mi/hr, horizontal = 163.39 mi/hr
D)vertical = 21.76 mi/hr, horizontal = 21.76 mi/hr
E)vertical = 26.56 mi/hr, horizontal = 163.39 mi/hr
with the horizontal, traveling at a speed of 165 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.A)vertical = 21.76 mi/hr, horizontal = 163.39 mi/hr
B)vertical = 163.39 mi/hr , horizontal = 163.39 mi/hr
C)vertical = 22.96 mi/hr, horizontal = 163.39 mi/hr
D)vertical = 21.76 mi/hr, horizontal = 21.76 mi/hr
E)vertical = 26.56 mi/hr, horizontal = 163.39 mi/hr
Question
The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is 
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. 
A)
B)
C)
D)
E)
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. A)
B)
C)
D)
E)
Question
Shown in the figure is a plan for the top of a wing of a jet fighter, where 
feet and 
feet. 
Approximate angle 
.
A)
B)
C)
D)
E)
feet and feet. Approximate angle .A)
B)
C)
D)
E)
Question
Solve 
A)
B)
C)
D)
E)No triangle exists
A)
B)
C)
D)
E)No triangle exists
Question
Express the complex number in trigonometric form with 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Question
Represent the complex number geometrically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve 
A)
B)
C)
D)
E)No triangle exists
A)
B)
C)
D)
E)No triangle exists
Question
The volume V of the right triangular prism shown in the figure is 
where B is the area of the base and h is the height of the prism. 
Approximate h, if 
.
A)15.6
B)15.2
C)4.3
D)16.0
E)14.0
where B is the area of the base and h is the height of the prism. Approximate h, if .A)15.6
B)15.2
C)4.3
D)16.0
E)14.0
Question
Find the two square roots of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A straight road makes an angle of 
with the horizontal. When the angle of elevation of the sun is 
, a vertical pole at the side of the road casts a shadow 
feet long directly down the road, as shown in the figure. 
Approximate the length of the pole.
A)121.00 ft
B)120.40 ft
C)79.77 ft
D)121.30 ft
E)120.10 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)121.00 ft
B)120.40 ft
C)79.77 ft
D)121.30 ft
E)120.10 ft
Question
Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure 
. 
A)120.1
B)119.2
C)147.1
D)120.8
E)123.4
. A)120.1
B)119.2
C)147.1
D)120.8
E)123.4
Question
Express in the form 
, where a and b are real numbers. 
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
Question
A helicopter hovers at an altitude that is 
feet above a mountain peak of altitude 5,847 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is 
, and from the mountaintop, the angle of elevation is 
. 
Approximate the altitude of the taller peak.
A)5,578 ft
B)6,118 ft
C)6,112 ft
D)6,116 ft
E)6,110 ft
feet above a mountain peak of altitude 5,847 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is , and from the mountaintop, the angle of elevation is . Approximate the altitude of the taller peak.A)5,578 ft
B)6,118 ft
C)6,112 ft
D)6,116 ft
E)6,110 ft
Question
Shown in the figure is a plan for the top of a wing of a jet fighter, where 
feet and 
feet. 
Approximate the area of triangle ABC.
A)442.7 ft 2
B)442.1 ft 2
C)885.0 ft 2
D)443.1 ft 2
E)442.5 ft 2
feet and feet. Approximate the area of triangle ABC.A)442.7 ft 2
B)442.1 ft 2
C)885.0 ft 2
D)443.1 ft 2
E)442.5 ft 2
Question
Express in the form 
, where a and b are real numbers. 
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
Question
A rhombus has sides of length 115 centimeters, and the angle at one of the vertices is 70 
. Approximate the lengths of the diagonals to the nearest tenth of a centimeter.
A)39.9 cm , 39.9 cm
B)142.1 cm , 187.6 cm
C)131.9 cm , 188.4 cm
D)142.1 cm , 188.2 cm
E)142.7 cm , 187.6 cm
. Approximate the lengths of the diagonals to the nearest tenth of a centimeter.A)39.9 cm , 39.9 cm
B)142.1 cm , 187.6 cm
C)131.9 cm , 188.4 cm
D)142.1 cm , 188.2 cm
E)142.7 cm , 187.6 cm
Question
Find || a ||. a = - < 3, - 9 >
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Represent the complex number geometrically. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use trigonometric forms to find 
and 
. 
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
Question
Find the two square roots of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Deck 8: Applications of Trigonometry
1
The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .
A)5.6
B)19.5
C)20.7
D)19.9
E)21.1
where B is the area of the base and h is the height of the prism. Approximate h, if .A)5.6
B)19.5
C)20.7
D)19.9
E)21.1
19.9
2
Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle , as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .
A)19.60
B)19.90
C)19.30
D)0
E)19.84
, as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .A)19.60
B)19.90
C)19.30
D)0
E)19.84
19.90
3
Express in the form , where a and b are real numbers.
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
4
Represent the complex number geometrically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.
A)101.34 ft
B)99.84 ft
C)100.74 ft
D)100.44 ft
E)66.74 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)101.34 ft
B)99.84 ft
C)100.74 ft
D)100.44 ft
E)66.74 ft
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6
Express the complex number in trigonometric form with .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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7
The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Express in the form , where a and b are real numbers.
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
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9
A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).
A)9.80 acres
B)10.13 acres
C)10.41 acres
D)3.13 acres
E)11.00 acres
). A)9.80 acres
B)10.13 acres
C)10.41 acres
D)3.13 acres
E)11.00 acres
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10
Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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11
If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
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12
A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is . When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.
A)737 ft
B)735 ft
C)1,610 ft
D)739 ft
E)733 ft
. When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.A)737 ft
B)735 ft
C)1,610 ft
D)739 ft
E)733 ft
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13
Find 2a + 5b. a = < 2, - 2>, b = <6, 2 >
A)2a + 5b = < 4, 11 >
B)2a + 5b = < 32, 10 >
C)2a + 5b = < 36, 8 >
D)2a + 5b = < 30, 10 >
E)2a + 5b = < 34, 6 >
A)2a + 5b = < 4, 11 >
B)2a + 5b = < 32, 10 >
C)2a + 5b = < 36, 8 >
D)2a + 5b = < 30, 10 >
E)2a + 5b = < 34, 6 >
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14
Find 2a - 3b. a = i + 2j, b = 3i - 5j
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Represent the complex number geometrically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Use trigonometric forms to find and .
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
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17
Determine m such that the two vectors are orthogonal. and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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18
Find the absolute value.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 145 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.
A)vertical = 22.53 mi/hr, horizontal = 143.76 mi/hr
B)vertical = 143.76 mi/hr , horizontal = 143.76 mi/hr
C)vertical = 17.73 mi/hr, horizontal = 143.76 mi/hr
D)vertical = 17.73 mi/hr, horizontal = 17.73 mi/hr
E)vertical = 18.93 mi/hr, horizontal = 143.76 mi/hr
with the horizontal, traveling at a speed of 145 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.A)vertical = 22.53 mi/hr, horizontal = 143.76 mi/hr
B)vertical = 143.76 mi/hr , horizontal = 143.76 mi/hr
C)vertical = 17.73 mi/hr, horizontal = 143.76 mi/hr
D)vertical = 17.73 mi/hr, horizontal = 17.73 mi/hr
E)vertical = 18.93 mi/hr, horizontal = 143.76 mi/hr
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20
If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and
A)2
B)4
C)26
D)7
E)-14
and A)2
B)4
C)26
D)7
E)-14
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21
The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .
A)6.2
B)22.6
C)23.0
D)22.2
E)21.0
where B is the area of the base and h is the height of the prism. Approximate h, if .A)6.2
B)22.6
C)23.0
D)22.2
E)21.0
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22
Represent the complex number geometrically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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23
A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 175 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.
A)vertical = 25.56 mi/hr, horizontal = 173.30 mi/hr
B)vertical = 173.30 mi/hr , horizontal = 173.30 mi/hr
C)vertical = 25.56 mi/hr, horizontal = 25.56 mi/hr
D)vertical = 24.36 mi/hr, horizontal = 173.30 mi/hr
E)vertical = 20.76 mi/hr, horizontal = 173.30 mi/hr
with the horizontal, traveling at a speed of 175 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.A)vertical = 25.56 mi/hr, horizontal = 173.30 mi/hr
B)vertical = 173.30 mi/hr , horizontal = 173.30 mi/hr
C)vertical = 25.56 mi/hr, horizontal = 25.56 mi/hr
D)vertical = 24.36 mi/hr, horizontal = 173.30 mi/hr
E)vertical = 20.76 mi/hr, horizontal = 173.30 mi/hr
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24
Represent the complex number geometrically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
Express the complex number in trigonometric form with .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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26
Find the absolute value.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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27
Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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28
If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and
A)32
B)14
C)44
D)-8
E)22
and A)32
B)14
C)44
D)-8
E)22
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29
Find the two square roots of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.
A)114.56 ft
B)113.36 ft
C)114.86 ft
D)114.26 ft
E)75.70 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)114.56 ft
B)113.36 ft
C)114.86 ft
D)114.26 ft
E)75.70 ft
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31
Find 4a + 3b. a = < 4, - 2>, b = <4, 5 >
A)4a + 3b = < 28, 7 >
B)4a + 3b = < 12, 15 >
C)4a + 3b = < 32, 12 >
D)4a + 3b = < 8, 7 >
E)4a + 3b = < 24, 17 >
A)4a + 3b = < 28, 7 >
B)4a + 3b = < 12, 15 >
C)4a + 3b = < 32, 12 >
D)4a + 3b = < 8, 7 >
E)4a + 3b = < 24, 17 >
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32
The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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33
Determine m such that the two vectors are orthogonal. and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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34
The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is . Approximate the unknown quantity, and express the answer in rectangular form to two decimal places.
A)
B)
C)
D)
E)
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. A)
B)
C)
D)
E)
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35
Find 5a - 2b. a = i + 4j, b = 6i - 6j
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).
A)10.89 acres
B)11.17 acres
C)3.39 acres
D)11.50 acres
E)10.30 acres
). A)10.89 acres
B)11.17 acres
C)3.39 acres
D)11.50 acres
E)10.30 acres
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37
A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is . When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.
A)605 ft
B)607 ft
C)601 ft
D)1,561 ft
E)599 ft
. When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.A)605 ft
B)607 ft
C)601 ft
D)1,561 ft
E)599 ft
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38
Find the two square roots of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle , as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .
A)0
B)7.23
C)7.17
D)7.20
E)7.99
, as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .A)0
B)7.23
C)7.17
D)7.20
E)7.99
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40
If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
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41
Express in the form , where a and b are real numbers.
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
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42
Express in the form , where a and b are real numbers.
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
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43
The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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44
The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is . Approximate the unknown quantity, and express the answer in rectangular form to two decimal places.
A)
B)
C)
D)
E)
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. A)
B)
C)
D)
E)
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45
Find 4a + 6b. a = < 5, - 4>, b = <6, 5 >
A)4a + 6b = < 9, 12 >
B)4a + 6b = < 61, 19 >
C)4a + 6b = < 56, 14 >
D)4a + 6b = < 36, 30 >
E)4a + 6b = < 51, 24 >
A)4a + 6b = < 9, 12 >
B)4a + 6b = < 61, 19 >
C)4a + 6b = < 56, 14 >
D)4a + 6b = < 36, 30 >
E)4a + 6b = < 51, 24 >
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46
Find the two square roots of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
Use trigonometric forms to find and .
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
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48
If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and
A)48
B)12
C)-24
D)-12
E)21
and A)48
B)12
C)-24
D)-12
E)21
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49
A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).
A)10.67 acres
B)11.00 acres
C)11.28 acres
D)3.27 acres
E)9.47 acres
). A)10.67 acres
B)11.00 acres
C)11.28 acres
D)3.27 acres
E)9.47 acres
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50
A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.
A)94.60 ft
B)94.90 ft
C)62.67 ft
D)94.00 ft
E)95.50 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)94.60 ft
B)94.90 ft
C)62.67 ft
D)94.00 ft
E)95.50 ft
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51
Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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52
A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is . When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.
A)1,200 ft
B)483 ft
C)487 ft
D)489 ft
E)481 ft
. When it is viewed at a distance of feet from the base of the hill, the angle of elevation is . The hill rises at an angle of . Approximate the height of the cathedral.A)1,200 ft
B)483 ft
C)487 ft
D)489 ft
E)481 ft
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53
The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .
A)4.9
B)18.8
C)18.4
D)18.0
E)17.6
where B is the area of the base and h is the height of the prism. Approximate h, if .A)4.9
B)18.8
C)18.4
D)18.0
E)17.6
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54
Determine m such that the two vectors are orthogonal. and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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55
Find the two square roots of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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56
Find the absolute value.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.B ) Find an additional force G such that equilibrium occurs.
A)
B)
C)
D)
E)
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58
Find 4a - 6b. a = i + 4j, b = 5i - 2j
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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59
Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle , as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .
A)24.74
B)26.99
C)25.50
D)26.28
E)0
, as shown in the figure. If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector .A)24.74
B)26.99
C)25.50
D)26.28
E)0
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60
A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 165 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.
A)vertical = 21.76 mi/hr, horizontal = 163.39 mi/hr
B)vertical = 163.39 mi/hr , horizontal = 163.39 mi/hr
C)vertical = 22.96 mi/hr, horizontal = 163.39 mi/hr
D)vertical = 21.76 mi/hr, horizontal = 21.76 mi/hr
E)vertical = 26.56 mi/hr, horizontal = 163.39 mi/hr
with the horizontal, traveling at a speed of 165 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.A)vertical = 21.76 mi/hr, horizontal = 163.39 mi/hr
B)vertical = 163.39 mi/hr , horizontal = 163.39 mi/hr
C)vertical = 22.96 mi/hr, horizontal = 163.39 mi/hr
D)vertical = 21.76 mi/hr, horizontal = 21.76 mi/hr
E)vertical = 26.56 mi/hr, horizontal = 163.39 mi/hr
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61
The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is . Approximate the unknown quantity, and express the answer in rectangular form to two decimal places.
A)
B)
C)
D)
E)
. Approximate the unknown quantity, and express the answer in rectangular form to two decimal places. A)
B)
C)
D)
E)
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62
Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate angle .
A)
B)
C)
D)
E)
feet and feet. Approximate angle .A)
B)
C)
D)
E)
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63
Solve
A)
B)
C)
D)
E)No triangle exists
A)
B)
C)
D)
E)No triangle exists
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64
Express the complex number in trigonometric form with .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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65
Find 3a + 6b. a = < 5, - 3>, b = <4, 6 >
A)3a + 6b = < 39, 27 >
B)3a + 6b = < 44, 33 >
C)3a + 6b = < 34, 39 >
D)3a + 6b = < 24, 36 >
E)3a + 6b = < 8, 10 >
A)3a + 6b = < 39, 27 >
B)3a + 6b = < 44, 33 >
C)3a + 6b = < 34, 39 >
D)3a + 6b = < 24, 36 >
E)3a + 6b = < 8, 10 >
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66
Represent the complex number geometrically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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67
Solve
A)
B)
C)
D)
E)No triangle exists
A)
B)
C)
D)
E)No triangle exists
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68
The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .
A)15.6
B)15.2
C)4.3
D)16.0
E)14.0
where B is the area of the base and h is the height of the prism. Approximate h, if .A)15.6
B)15.2
C)4.3
D)16.0
E)14.0
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69
Find the two square roots of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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70
A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.
A)121.00 ft
B)120.40 ft
C)79.77 ft
D)121.30 ft
E)120.10 ft
with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.A)121.00 ft
B)120.40 ft
C)79.77 ft
D)121.30 ft
E)120.10 ft
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71
Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure .
A)120.1
B)119.2
C)147.1
D)120.8
E)123.4
. A)120.1
B)119.2
C)147.1
D)120.8
E)123.4
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72
Express in the form , where a and b are real numbers.
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
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73
A helicopter hovers at an altitude that is feet above a mountain peak of altitude 5,847 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is , and from the mountaintop, the angle of elevation is . Approximate the altitude of the taller peak.
A)5,578 ft
B)6,118 ft
C)6,112 ft
D)6,116 ft
E)6,110 ft
feet above a mountain peak of altitude 5,847 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is , and from the mountaintop, the angle of elevation is . Approximate the altitude of the taller peak.A)5,578 ft
B)6,118 ft
C)6,112 ft
D)6,116 ft
E)6,110 ft
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74
Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate the area of triangle ABC.
A)442.7 ft 2
B)442.1 ft 2
C)885.0 ft 2
D)443.1 ft 2
E)442.5 ft 2
feet and feet. Approximate the area of triangle ABC.A)442.7 ft 2
B)442.1 ft 2
C)885.0 ft 2
D)443.1 ft 2
E)442.5 ft 2
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75
Express in the form , where a and b are real numbers.
A)
B)
C)
D)
E)
, where a and b are real numbers. A)
B)
C)
D)
E)
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76
A rhombus has sides of length 115 centimeters, and the angle at one of the vertices is 70 . Approximate the lengths of the diagonals to the nearest tenth of a centimeter.
A)39.9 cm , 39.9 cm
B)142.1 cm , 187.6 cm
C)131.9 cm , 188.4 cm
D)142.1 cm , 188.2 cm
E)142.7 cm , 187.6 cm
. Approximate the lengths of the diagonals to the nearest tenth of a centimeter.A)39.9 cm , 39.9 cm
B)142.1 cm , 187.6 cm
C)131.9 cm , 188.4 cm
D)142.1 cm , 188.2 cm
E)142.7 cm , 187.6 cm
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77
Find || a ||. a = - < 3, - 9 >
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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78
Represent the complex number geometrically.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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79
Use trigonometric forms to find and .
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
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80
Find the two square roots of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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