Deck 7: Applications of Trigonometry

Question 1

Solve the triangle with the given parts.

A) = 26.4°, a = 26.28, c = 54.24
B) = 26.4°, a = 28.28, c = 56.24
C) = 24.4°, a = 56.24, c = 28.28
D) = 24.4°, a = 54.24, c = 26.28

Answer 1

= 26.4°, a = 26.28, c = 54.24

Question 2

Determine the number of triangles with the given parts.
a = 24, b = 20, = 47°

A) 1
B) 0
C) 3
D) 2

Answer 2

1

Question 3

Solve the triangle with the given parts.

A) = 21.7°, a = 16.9, c = 40.3
B) = 19.7°, a = 38.3, c = 14.9
C) = 21.7°, a = 14.9, c = 38.3
D) = 19.7°, a = 40.3, c = 16.9

Answer 3

= 21.7°, a = 14.9, c = 38.3

Question 4

Solve the triangle with the given parts.

A) 97°, a = 12.4, b = 21.9
B) = 103°, a = 22.3, b = 12.6
C) = 103°, a = 62.2, b = 35.1
D) = 103°, a = 12.6, b = 22.3

Question 5

Solve the triangle with the given parts.
= 37.9°, b = 16.3, = 93.4°

A) = 131.3°, a = 13.3, c = 21.7
B) = 48.7°, a = 10, c = 4.6
C) = 48.7°, a = 13.3, c = 21.7
D) = 131.3°, a = 10, c = 4.6

Question 6

Determine the number of triangles with the given parts.
b = 41, c = 51, = 102°

A) 3
B) 1
C) 2
D) 0

Question 7

Approximate the area of the triangle to the nearest tenth.

A) 1380.1
B) 1401.2
C) 1388.4
D) 1371.6

Question 8

Determine the number of triangles with the given parts.
a = 15, b = 25, = 93°

A) 3
B) 2
C) 1
D) 0

Question 9

Approximate the area of the triangle to the nearest tenth.
= 48.3°, b = 87, c = 12.7

A) 412.5
B) 408.3
C) 427.6
D) 421.8

Question 10

Solve the triangle. If there is more than one triangle with the given parts, give both solutions.
= 10.1° b = 12.05
A = 17.18

A) No solution
B)
C)
D)

Question 11

Solve the triangle with the given parts.

A) = 37.2°, b = 30.9, c = 25.2
B) = 37.2°, b = 371.1, c = 300.1
C) = 37.2°, b = 300.1, c = 371.1
D) = 36.8°, b = 297.3, c = 371.1

Question 12

Determine the number of triangles with the given parts.
b = 24, c = 27, = 44°

A) 1
B) 0
C) 2
D) 3

Question 13

Solve the triangle with the given parts.
= 50.2°, = 40.3°, a = 22.7

A) = 89.5°, b = 29.6, c = 19.1
B) = 90.5°, b = 19.1, c = 29.6
C) 90.5°, b = 29.6, c = 19.1
D) = 89.5°, b = 19.1, c = 29.6

Question 14

Determine the number of triangles with the given parts.
a = 34, b = 69, = 74°

A) 0
B) 3
C) 1
D) 2

Question 15

Approximate the area of the triangle to the nearest tenth.
= 60.8°, a = 36.2, c = 75.4

A) 1187.1
B) 1191.3
C) 1206.4
D) 1200.6

Question 16

Solve the triangle. If there is more than one triangle with the given parts, give both solutions.
= 30.0° a = 21.18
B = 42.36

A)
B) No solution
C)
D)

Question 17

Solve the triangle. If there is more than one triangle with the given parts, give both solutions.
= 31.7° b = 13.12
A = 24.0

A)
B) No solution
C)
D)

Question 18

Solve the triangle. If there is more than one triangle with the given parts, give both solutions.
= 16.31° b = 15.45
A = 18.34

A) No solution
B)
C)
D)

Question 19

Solve the triangle. If there is more than one triangle with the given parts, give both solutions.
= 16.6° b = 9.52
A = 18.9

A)
B)
C)
D)

Question 20

Determine the number of triangles with the given parts.
a = 35, b = 46, = 26°

A) 0
B) 3
C) 2
D) 1

Question 21

Solve the triangle. Approximate values to the nearest tenth when appropriate.

A)
B)
C)
D) No solution

Question 22

Find the area of the region.
Round to the nearest square foot.

A)
B)
C)
D)

Question 23

Solve the triangle. Approximate values to the nearest tenth when appropriate.
= 116.1° a = 6.40
B = 11.77

A)
B) No solution
C)
D)

Question 24

Solve.
Two tracking stations are on the equator 151 miles apart. A weather balloon is located on a bearing of N 41°E from the western station and on a bearing of N 18°E from the eastern station. How far is the balloon from the
Western station? Round to the nearest mile.

A) 322 mi
B) 331 mi
C) 368 mi
D) 377 mi

Question 25

Solve the triangle. Approximate values to the nearest tenth when appropriate.
= 120.75° b = 4.70
A = 12.20

A)
B)
C) No solution
D)

Question 26

Solve.
A homeowner wants to fence in a triangular garden. One side of the garden is edged by a brick wall and 20 feet of fencing is purchased to fence in the other two sides. The angle that one edge of the garden makes with the
Wall is 20° and 12 feet of fencing is needed for this edge. Is there enough fencing left to edge the second side?

A) No
B) Yes

Question 27

Approximate the area of the triangle to the nearest tenth.

A) 343.4
B) 132.7
C) 204.4
D) 171.7

Question 28

Solve.
A triangular-shaped field has sides of 197.5 m and 193.4 m, and the angle between them measures 61.63°. Find the area of the field to the nearest square meter.

A)
B)
C)
D)

Question 29

Solve.
A boat leaves the dock and sails in a direction of 70°. Once reaching its destination on the opposite shore, it sails in a direction of 272° and docks 150 km north of its original starting position. What is the total distance the boat
Has traveled? Round to the nearest kilometer.

A) 626 km
B) 776 km
C) 997 km
D) 926 km

Question 30

Solve.
To find the distance AB across a river, a distance BC of 756 m is laid off on one side of the river. It is found that B = 109.4° and C = 13.9°. Find AB rounded to the nearest meter.

A) 220 m
B) 179 m
C) 182 m
D) 217 m

Question 31

Find the area of the region.
Round to the nearest hundredth of a square foot.

A)
B)
C)
D)

Question 32

Solve.
A ranger in fire tower A spots a fire at a direction of 40°. A ranger in fire tower B, which is 28 miles directly east of tower A, spots the same fire at a direction of 116°. How far from tower A is the fire? Round to the nearest
Mile.

A) 26 mi
B) 33 mi
C) 22 mi
D) 24 mi

Question 33

Solve the triangle. Approximate values to the nearest tenth when appropriate.
a = 6.2 b = 13.3
C = 15.9

A)
B) No solution
C)
D)

Question 34

Solve the triangle. Approximate values to the nearest tenth when appropriate.
= 122.5° a = 5.30
B = 10.18

A)
B)
C) No solution
D)

Question 35

Solve the triangle. Approximate values to the nearest tenth when appropriate.

A)
B)
C)
D) No solution

Question 36

Determine the number of triangles with the given parts.
a = 4, b = 7, c = 11

A) 0
B) 1
C) 2
D) 3

Question 37

Solve the triangle. Approximate values to the nearest tenth when appropriate.
= 63.5° a = 12.20
C = 7.80

A)
B)
C)
D) No solution

Question 38

Solve.
A guy wire to a tower makes a 69° angle with level ground. At a point 34 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is 32°. Find the length
Of the wire (to the nearest foot).

A) 65 ft
B) 35 ft
C) 60 ft
D) 30 ft

Question 39

Solve the triangle. Approximate values to the nearest tenth when appropriate.
a = 6.9 b = 13.6
C = 15.9

A)
B)
C)
D) No solution

Question 40

Approximate the area of the triangle to the nearest tenth.
= 37.6°, b = 11.2, a = 12.1

A) 64.4
B) 41.3
C) 67.8
D) 38.3

Question 41

Solve.
A plane flying a straight course observes a mountain at a bearing of 30.1° to the right of its course. At that time the plane is 6 km from the mountain. A short time later, the bearing to the mountain becomes 40.1°. How far is
The plane from the mountain when the second bearing is taken (to the nearest tenth of a km)?

A) 3.1 km
B) 7.7 km
C) 8.8 km
D) 4.7 km

Question 42

Approximate the area of the triangle to the nearest tenth.

A) 2801
B) 2780
C) 1552
D) 1551

Question 43

Solve.
Two boats leave a dock together, each traveling in a straight line. One boat travels at 28 mph and the other at 26 mph. The angle between their courses measures 28.7°. Approximate the distance, to the nearest tenth of a
Mile, between the boats after 46 minutes.

A) 22.0 mi
B) 35.1 mi
C) 10.4 mi
D) 40.1 mi

Question 44

Approximate the area of the triangle to the nearest tenth.
a = 150, b = 164, c = 170

A) 13,977.4
B) 11,181.9
C) 718.8
D) 16,772.9

Question 45

Approximate the area of the triangle to the nearest tenth.
18.8
12.6
17.0

A) 104
B) 113
C) 110
D) 107

Question 46

Solve.
A ship travels 81 km on a bearing of 29°, and then travels on a bearing of 119° for 164 km. To the nearest kilometer, find the distance from the start to the end of the trip.

A) 183 km
B) 39 km
C) 245 km
D) 71 km

Question 47

Solve.
The sides of a parallelogram are 12 ft and 14 ft. One angle is 40° while another angle is 140°. Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).

A) 16.8 ft and 9.1 ft
B) 9.1 ft and 24.4 ft
C) 14.5 ft and 21.6 ft
D) 82.6 ft and 597.4 ft

Question 48

Approximate the area of the triangle to the nearest tenth.
a = 8.5, b = 16.2, c = 15.4

A) 73.4
B) 70.4
C) 67.4
D) 64.4

Question 49

The vectors u, v, and w are drawn below. Sketch the given vector.
u + v

A)
B)
C)
D)

Question 50

Solve.
Two ships leave a harbor together traveling on courses that have an angle of 128° between them. If they each travel 544 miles, how far apart are they (to the nearest mile)?

A) 42 mi
B) 1956 mi
C) 477 mi
D) 978 mi

Question 51

Determine the number of triangles with the given parts.
a = 4, b = 8, c = 11

A) 0
B) 1
C) 2
D) 3

Question 52

Solve.
Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 70 yd from B and 103 yd from A, with angle ACB measuring 69.3°. How far apart are A and B (to the nearest yard)?

A) 120 yd
B) 129 yd
C) 102 yd
D) 111 yd

Question 53

Solve.
To find the distance between two small towns, an electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible. The distance from the EDM to the towns is 2.6 miles and 2.7 miles and
The angle between the two lines of sight is 41°. Find the distance between the towns to the nearest tenth of a
Mile.

A) 5.0 mi
B) 1.9 mi
C) 4.4 mi
D) 3.0 mi

Question 54

Solve.
A tower is supported by a guy wire 471 feet long. The wire makes an angle of 70° with respect to the ground, and the distance from the point where the wire is attached to the ground and the tower is 218 feet. Approximate
The height of the tower to the nearest tenth of a foot.

A) 582.8 ft
B) 446.2 ft
C) 484.0 ft
D) 551.8 ft

Question 55

Determine the number of triangles with the given parts.

A) 0
B) 1
C) 2
D) 3

Question 56

Approximate the area of the triangle to the nearest tenth.
a = 43, b = 52, c = 60

A) 1365.4
B) 1638.5
C) 1092.3
D) 124.1

Question 57

Solve.
Two airplanes leave an airport at the same time, one going northwest at 405 mph and the other going east at 343 mph. How far apart are the planes after 2 hours (to the nearest mile)?

A) 691 mi
B) 1233 mi
C) 1150 mi
D) 1383 mi

Question 58

Determine the number of triangles with the given parts.

A) 0
B) 1
C) 2
D) 3

Question 59

Approximate the area of the triangle to the nearest tenth.

A) 336.6
B) 345.9
C) 351.7
D) 332.4

Question 60

Approximate the area of the triangle to the nearest tenth.

A) 747.9
B) 752.1
C) 767.2
D) 761.4

Question 61

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
2, 2

A) 4; 45°
B) 2; 225°
C)
D)

Question 62

The vectors u, v, and w are drawn below. Sketch the given vector.
u - v

A)
B)
C)
D)

Question 63

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction
angle Round to the nearest tenth.

A)
B)
C)
D)

Question 64

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-20, 0

A) 400; 180°
B) 20; 270°
C) 20; 180°
D) 20; 90°

Question 65

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].

A) 36; 30°
B) 36; 150°
C) 18; 150°
D) 18; 330°

Question 66

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].

A) 14; 344.5°
B) 14; 105.5°
C)
D)

Question 67

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-4, -3

A) 7; 216.9°
B) 5; 216.9°
C) 5; 36.9°
D) 5; 233.1°

Question 68

The vectors u, v, and w are drawn below. Sketch the given vector.
u + w

A)
B)
C)
D)

Question 69

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction
angle Round to the nearest tenth.

A)
B)
C)
D)

Question 70

The vectors u, v, and w are drawn below. Sketch the given vector.
w - v

A)
B)
C)
D)

Question 71

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].

A) 4; 135°
B) 4; 315°
C) 8; 315°
D)

Question 72

Find the component form for the vector with the given magnitude and direction angle . Round values to the nearest
tenth.

A) 100.6, 64.6
B) -100.6, -64.6
C) -64.6, -100.6
D) 64.6, 100.6

Question 73

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].

A) 40; 45°
B)
C) 20; 45°
D) 20; 225°

Question 74

The vectors u, v, and w are drawn below. Sketch the given vector.
v + w

A)
B)
C)
D)

Question 75

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-5, 12

A) 15; 112.6°
B) 13; 157.4°
C) 13; 67.4°
D) 13; 112.6°

Question 76

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].

A) 28; 30°
B) 14; 30°
C) 14; 150°
D)

Question 77

Determine which of the position vectors shown in the figure below has the given magnitude and direction angle.
Magnitude 2 and direction angle 150°

A) E
B) C
C) D
D) B

Question 78

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
0, -2

A) 2; 90°
B) 2; 180°
C) 4; 270°
D) 2; 270°

Question 79

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction
angle Round to the nearest tenth.

A)
B)
C)
D)

Question 80

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction
angle Round to the nearest tenth.

A)
B)
C)
D)