Deck 7: Triangles

Question 1

The problem that follows refers to triangle ABC . ​ If  and  km, find C  and c
Apply the rules regarding the use of significant digits after all computations are complete.
​

A)  km
B) ​ km
C) ​ km
D)​ km
E) ​ km

Answer 1

​ km

Question 2

The information below refers to triangle ABC . ​ ​ Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete.
​

A)​B ​ = 27°,  ​b ​ = 2.14 ft, c = 8.33 ft
B)B ​ = 26 °,  ​b ​ = 2.04  ft,  c  = 4.21  ft
C)B ​ = 26 °,  ​b ​ = 2.04  ft,  c  = 4.41  ft
D)B ​ = 24 °,  ​b ​ = 9.03  ft,  c  = 8.33  ft
E)​B ​ =  27 °,  ​b ​ =  2.14  ft,   c  = 4.41  ft

Answer 2

​B ​ =  27 °,  ​b ​ =  2.14  ft,   c  = 4.41  ft

Question 3

A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is b ​ = 67°. He then walks 100 feet further away and observes that the angle of elevation to the top of the antenna is ​a ​ = 45° . Find the height of the antenna to the nearest foot. ( Hint : Find x first.)​ ​

A)  ft
B)  ft
C)  ft
D)  ft
E)  ft

Answer 3

 ft

Question 4

A 140-foot antenna is on top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 27.5°, while the angle of elevation to the bottom of the antenna from the same point is 22.5°. How tall is the building? Please round to the nearest foot. ​

A)549 ft
B)546 ft
C)545 ft
D)543 ft
E)548 ft

Question 5

The information below refers to triangle ABC .  inches. Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete.
​

A)  inches,  inches
B)  inches,  inches
C)  inches,  inches
D)  inches,  inches
E)  inches,  inches

Question 6

A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 50°. She rides the elevator up three floors (60 feet)and finds that the angle of elevation to the top of the building across the street is 34°. How tall is the building across the street? (Give your answer to the nearest foot.) ​

A)139 ft
B)138 ft
C)141 ft
D)136 ft
E)142 ft

Question 7

The problem that follows refers to triangle ABC . ​ If  and  inches, find b
Apply the rules regarding the use of significant digits.
​

A)148 inches
B)160 inches
C)150 inches
D)154 inches
E)138 inches

Question 8

The information below refers to triangle ABC .  inches. Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete.
​

A)  inches,  inches
B)  inches,  inches
C)  inches,  inches
D)  inches,  inches
E)  inches,  inches

Question 9

The problem that follows refers to triangle ABC . ​ If  and  cm, find C  and a
Apply the rules regarding the use of significant digits after all computations are complete.
​

A)  cm
B)  cm
C)  cm
D)  cm
E)  cm

Question 10

A man is flying in a hot-air balloon in a straight line at a constant rate of 4 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 35°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36°. At that time, what is the distance between him and his friend? (Give your answer to the nearest foot.) ​

A)214 ft
B)221 ft
C)219 ft
D)218 ft
E)216 ft

Question 11

A tightrope walker is standing still with one foot on the tightrope as shown in the figure. If the tightrope walker weighs 123 pounds, find the magnitudes of the tension in the rope toward each end of the rope. Apply the rules regarding the use of significant digits after all computations are complete. ​ ​

A)  lbs,  lbs
B)  lbs,  lbs
C)  lbs,  lbs
D)  lbs,  lbs
E)  lbs,  lbs

Question 12

The information below refers to triangle ABC .  m. Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete.
​

A)  m,  m
B)  m,  m
C)  m,  m
D)  m,  m
E)  m,  m

Question 13

A ship is anchored off a long straight shoreline that runs north and south. From two observation points 20 miles apart on shore, the bearings of the ship are N 28° E and S 53° E. What is the distance from the ship to each of the observation points? Apply the rules regarding the use of significant digits after all computations are complete.

A)16 miles and 11.5 miles
B)14 miles and 9.5 miles
C)14 miles and 11.5 miles
D)17 miles and 8.0 miles
E)16 miles and 9.5 miles

Question 14

The problem that follows refers to triangle ABC . ​ If  and  yd, find a
Apply the rules regarding the use of significant digits after all computations are complete.
​

A)49.1 yd
B)56.1 yd
C)53.1 yd
D)55.1 yd
E)54.1 yd

Question 15

The circle in the figure below has a radius of r and center at C . The distance from A to B is x , the distance from A to D is y , and the length of arc BD is s . For the following problem, redraw the figure, label it with the values given, and then solve. ​ If  and  find y . Apply the rules regarding the use of significant digits after all computations are complete. ​

A)
B)
C)
D)
E)

Question 16

If you have ever ridden on a chair lift at a ski area and had it stop, you know that the chair will pull down on the cable, dropping you down to a lower height then when the chair is in motion. The figure shows a gondola that is stopped. Find the magnitude of the tension in the cable toward each end of the cable if the total weight of the gondola and its occupants is 1,900 pounds. Apply the rules regarding the use of significant digits after all computations are complete. ​a ​ = 71.6,  ​b ​ = 74.6 ​ ​

A)
B)​
C)​
D)​
E)​

Question 17

The problem that follows refers to triangle ABC . ​ If  and  cm, find a
Apply the rules regarding the use of significant digits.
​

A)23 cm
B)​24 cm
C)19​ cm
D)18​ cm
E)20​ cm

Question 18

The problem that follows refers to triangle ABC . ​ If  and  inches, find c
Apply the rules regarding the use of significant digits after all computations are complete.
​

A)6.0 inches
B)9 inches
C)11 inches
D)8.0 inches
E)12 inches

Question 19

The circle in the figure below has a radius of r and center at C . The distance from A to B is x , the distance from A to D is y , and the length of arc BD is s . For the following problem, redraw the figure, label it with the values given, and then solve. ​If  and , find x . Apply the rules regarding the use of significant digits after all computations are complete. ​

A)
B)
C)
D)
E)

Question 20

The information below refers to triangle ABC .  cm ​Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete.
​

A)​
B)​
C)​
D)​
E)​

Question 21

The circle in the figure below has a radius of r and center at C . The distance from A to B is x , the distance from A to D is y , and the length of arc BD is s . For the following problem, redraw the figure, label it with the values given, and then solve. ​ If  and  find x . Apply the rules regarding the use of significant digits after all computations are complete. ​ __________

Question 22

The problem that follows refers to triangle ABC .​ If  and  cm, find C  and a . Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________ cm

Question 23

The problem that follows refers to triangle ABC . If  and  inches, find b . Apply the rules regarding the use of significant digits after all computations are complete. __________ inches

Question 24

The circle in the figure below has a radius of r and center at C . The distance from A to B is x , the distance from A to D is y , and the length of arc BD is s . For the following problem, redraw the figure, label it with the values given, and then solve.
​ If  and  find y . Apply the rules regarding the use of significant digits after all computations are complete. ​ __________

Question 25

The information below refers to triangle ABC . ​
Find B , b , and c . Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________ ft ​ __________ ft

Question 26

The information below refers to triangle ABC .​ If  inches, find C , b  and c . Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________ inches ​ __________ inches

Question 27

The information below refers to triangle ABC . ​
Apply the rules regarding the use of significant digits after all computations are complete.
Find A , b , and c . __________° ​ __________ cm ​ __________ cm

Question 28

A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is ​b ​ = 63°. He then walks 100 feet further away and observes that the angle of elevation to the top of the antenna is ​a ​ = 42°. Find the height of the antenna to the nearest foot. ( Hint : Find x  first.)​ ​ __________ ft

Question 29

A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 36°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 37°. At that time, what is the distance between him and his friend? (Give your answer to the nearest foot.)
Distance = __________ ft

Question 30

If you have ever ridden on a chair lift at a ski area and had it stop, you know that the chair will pull down on the cable, dropping you down to a lower height then when the chair is in motion. The figure shows a gondola that is stopped. Find the magnitude of the tension in the cable toward each end of the cable if the total weight of the gondola and its occupants is 1880 pounds. Apply the rules regarding the use of significant digits after all computations are complete.​
​a ​ = 71.8,  ​b ​ = 75.8 ​ ​ __________ lbs ​ __________ lbs

Question 31

The information below refers to triangle ABC . ​ If  m, find A , b , and c . __________° ​ __________ m ​ __________ m

Question 32

The problem that follows refers to triangle ABC .​ If  and  yd, find a . Apply the rules regarding the use of significant digits after all computations are complete. __________ yd

Question 33

A ship is anchored off a long straight shoreline that runs north and south. From two observation points 18 miles apart on shore, the bearings of the ship are N 26° E and S 51° E. What is the distance from the ship to each of the observation points?
​Apply the rules regarding the use of significant digits after all computations are complete. The distance from the ship to the observation point for which the bearing of the ship is N 26° E is __________ mi The distance from the ship to the observation point for which the bearing of the ship is S 51° E is __________ mi

Question 34

A tightrope walker is standing still with one foot on the tightrope as shown in the figure. If the tightrope walker weighs 124 pounds, find the magnitudes of the tension in the rope toward each end of the rope. Apply the rules regarding the use of significant digits after all computations are complete. ​a ​ = 75.5​,  ​b ​ = 81.5 ​ ​ __________ lbs ​ __________ lbs

Question 35

A 140-foot antenna is on top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 27.5°, while the angle of elevation to the bottom of the antenna from the same point is 22.5°. How tall is the building? (Give your answer to the nearest foot.)
Height of building = __________ ft

Question 36

The problem that follows refers to triangle ABC .​ If  and  km , find   C and c . Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________ km

Question 37

The information below refers to triangle ABC . If   inches, find B , a , and b . Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________ inches ​ __________ inches

Question 38

The problem that follows refers to triangle ABC . If  and  cm, find a . Apply the rules regarding the use of significant digits after all computations are complete. __________ cm

Question 39

A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 50°. She rides the elevator up three floors (70 feet)and finds that the angle of elevation to the top of the building across the street is 34°. How tall is the building across the street? (Give your answer to the nearest foot.)
Height of building = __________ ft

Question 40

The problem that follows refers to triangle ABC .​ If  and  inches, find c . Apply the rules regarding the use of significant digits after all computations are complete. __________ inches

Question 41

Solve the triangle. ft, ft, ft Apply the rules regarding the use of significant digits after all computations are complete. ​

A)
B)​
C)​
D)​
E)​

Question 42

Solve the triangle. ​ km,  km,  ​ Apply the rules regarding the use of significant digits after all computations are complete.
​

A)  km
B)  km
C)  km
D)  km
E)  km

Question 43

Solve the triangle. ​ ​
Apply the rules regarding the use of significant digits after all computations are complete.
​

A)
B)​
C)​
D)​
E)​

Question 44

Refer to triangle ABC . If m, m, and , find b . Apply the rules regarding the use of significant digits after all computations are complete. ​

A)4.3 m
B)4.5 m
C)3.5 m
D)3.7 m
E)3.3 m

Question 45

Two ships leave a harbor entrance at the same time. The first ship is traveling at a constant 19 miles per hour, while the second is traveling at a constant 23 miles per hour. If the angle between their courses is 121°, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete.

A)71 mi
B)67 mi
C)65 mi
D)73 mi
E)77 mi

Question 46

Two planes take off at the same time from an airport. The first plane is flying at 246 miles per hour on a course of 130.0°. The second plane is flying in the direction 165.0° at 359 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete.

A)423 miles
B)421 miles
C)427 miles
D)431 miles
E)429 miles

Question 47

A plane is flying with an airspeed of 160 miles per hour and heading of 140°. The wind currents are running at 41 miles per hour at 155° clockwise from due north. Use vectors to find the true course and ground speed of the plane. Apply the rules regarding the use of significant digits after all computations are complete.

A)196 mph with heading 147°
B)200 mph with heading 145°
C)190 mph with heading 143°
D)190 mph with heading 145°
E)200 mph with heading 143°

Question 48

Refer to triangle ABC . If inches, inches, and , find c . Apply the rules regarding the use of significant digits after all computations are complete.
​

A)120 inches
B)140 inches
C)96 inches
D)110 inches
E)130 inches

Question 49

The diagonals of a parallelogram are 24 meters and 40 meters and intersect at an angle of 60°. Find the length of the longer side. ​

A)29 meters
B)28 meters
C)31 meters
D)26 meters
E)24 meters

Question 50

A plane has an airspeed of 175 miles per hour and heading of 30.0°. The ground speed of the plane is 206 miles per hour, and its true course is the direction of 34.0°. Find the speed and direction of the air currents, assuming they are constants. Apply the rules regarding the use of significant digits after all computations are complete.

A)33.3 mph at 55.2° from due to north
B)33.3 mph at 54.8° from due to north
C)33.7 mph at 54.8° from due to north
D)33.7 mph at 55.2° from due to north
E)34.5 mph at 54.4° from due to north

Question 51

A plane is flying with an airspeed of 245 miles per hour with heading 276.2°. The wind currents are running at a constant 47.2 miles per hour in the direction 266.1°. Find the ground speed and true course of the plane. Apply the rules regarding the use of significant digits after all computations are complete.

A)292 mph with heading 274.6°
B)302 mph with heading 274.6°
C)292 mph with heading 273.8°
D)292 mph with heading 294.6°
E)302 mph with heading 294.6°

Question 52

Refer to triangle ABC . If m, m, and , find a . Apply the rules regarding the use of significant digits after all computations are complete. ​

A)8.5 m
B)9.9 m
C)9.5 m
D)9.3 m
E)8.9 m

Question 53

Solve the triangle.  km,   km,  ​ Apply the rules regarding the use of significant digits after all computations are complete.
​

A)   km
B)  km
C)  km
D)  km
E)  km

Question 54

Use the law of cosines to find a true statement from the list below, if . ​

A)
B)​
C)​
D)​
E)​

Question 55

Refer to triangle ABC . If yd, yd, and yd, find the largest angle. Apply the rules regarding the use of significant digits after all computations are complete. __________°

Question 56

Two planes leave an airport at the same time. Their speeds are 140 miles per hour and 150 miles per hour, and the angle between their courses is 38°. How far apart are they after 1.5 hours?​ Apply the rules regarding the use of significant digits after all computations are complete.

A)182 mi
B)140 mi
C)150 mi
D)120 mi
E)112 mi

Question 57

Refer to triangle ABC . If cm, cm, and cm, find the largest angle. Apply the rules regarding the use of significant digits after all computations are complete. ​

A)
B)​
C)​
D)​
E)​

Question 58

Solve the triangle. ​ Apply the rules regarding the use of significant digits after all computations are complete.
​

A)
B)​
C)​
D)​
E)​

Question 59

Solve the triangle. ​Apply the rules regarding the use of significant digits after all computations are complete. ​

A)
B)​
C)​
D)​
E)​

Question 60

Refer to triangle ABC . If yd, yd, and yd, find the largest angle. Apply the rules regarding the use of significant digits after all computations are complete. ​

A)​
B)​
C)​
D)​
E)​

Question 61

For the triangle described below, solve for B . Apply the rules regarding the use of significant digits to each angle and length after all computations are complete.  ft,   ft
​

A)  or 
B)
C)  or 
D)
E)no solution

Question 62

Solve the triangle. m, m, ​
Apply the rules regarding the use of significant digits after all computations are complete. __________ m ​ __________° ​ __________°

Question 63

The diagonals of a parallelogram are 12 meters and 20 meters and intersect at an angle of 60°. Find the length of the longer side. __________ m

Question 64

Solve the triangle. yd, yd, yd
​
Apply the rules regarding the use of significant digits after all computations are complete. __________° ​ __________° ​ __________°

Question 65

Solve the triangle. km, km, ​
Apply the rules regarding the use of significant digits after all computations are complete. __________ km ​ __________°__________' ​ __________°__________'

Question 66

Refer to triangle ABC . If cm, cm, and cm, find the largest angle. Apply the rules regarding the use of significant digits after all computations are complete. __________°

Question 67

For the triangle described below, solve for B . Apply the rules regarding the use of significant digits after all computations are complete.  ft,   ft
​

A)
B)  or 
C)
D)  or 
E)no solutions

Question 68

A plane is flying with an airspeed of 170 miles per hour and heading of 150°. The wind currents are running at 36 miles per hour at 165° clockwise from due north. Use vectors to find the true course and ground speed of the plane. Apply the rules regarding the use of significant digits after all computations are complete. __________ mph with heading __________°

Question 69

Use the law of cosines to show that, if , then .

Question 70

Two planes leave an airport at the same time. Their speeds are 140 miles per hour and 150 miles per hour, and the angle between their courses is 33°. How far apart are they after 1.5 hours? Apply the rules regarding the use of significant digits after all computations are complete. __________ mi

Question 71

Two planes take off at the same time from an airport. The first plane is flying at 244 miles per hour on a course of 135.0°. The second plane is flying in the direction 170.0° at 358 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete. __________ mi

Question 72

Solve the triangle. km, km, ​
Apply the rules regarding the use of significant digits after all computations are complete. __________ km ​ __________°__________' ​ __________°__________'

Question 73

Solve the triangle. ft, ft, ft
Apply the rules regarding the use of significant digits after all computations are complete.
A = __________°
B = __________°
C = __________°

Question 74

Refer to triangle ABC . If m, m, and , find b .
Apply the rules regarding the use of significant digits after all computations are complete. __________ m

Question 75

Two ships leave a harbor entrance at the same time. The first ship is traveling at a constant 17 miles per hour, while the second is traveling at a constant 20 miles per hour. If the angle between their courses is 123°, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete. __________ mi

Question 76

Solve the triangle. m, m, ​
Apply the rules regarding the use of significant digits after all computations are complete. __________ m ​ __________° ​ __________°

Question 77

A plane is flying with an airspeed of 243 miles per hour with heading 271.7°. The wind currents are running at a constant 44.7 miles per hour in the direction 261.6°. Find the ground speed and true course of the plane. Apply the rules regarding the use of significant digits after all computations are complete. __________ mph with heading __________°

Question 78

Refer to triangle ABC . If inches, inches, and , find c . Apply the rules regarding the use of significant digits after all computations are complete. __________ inches

Question 79

A plane has an airspeed of 175 miles per hour and heading of 30.0°. The ground speed of the plane is 206 miles per hour, and its true course is the direction of 34.0°. Find the speed and direction of the air currents, assuming they are constants. Apply the rules regarding the use of significant digits after all computations are complete.​
__________ mph at __________° from due to north

Question 80

Refer to triangle ABC . If m, m, and , find a . Apply the rules regarding the use of significant digits after all computations are complete. __________ m