Deck 13: Right Triangle Trigonometry

Question 1

The angle opposite side k is _____.

A) ∠K
B) ∠L
C) ∠M

Answer 1

∠K

Question 2

Find the value of the trigonometric ratio rounded to four significant digits. sin 36.66 ^o

A) 0.7443
B) 1.675
C) 1.344
D) 0.8022
E) 0.5971

Answer 2

0.5971

Question 3

Find the value of the trigonometric ratio rounded to four significant digits. tan 11.40 ^o

A) 0.1977
B) 0.2016
C) 4.959
D) 0.9803
E) 5.059

Answer 3

0.2016

Question 4

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side. d = 48,500 m, e = 40,100 m
The unknown side f is _____ m.

A) 82,300
B) 8,860,000
C) 62,900
D) 27,300
E) 53,200

Question 5

Find the value of the trigonometric ratio rounded to four significant digits. sin 65.8 ^o

A) 0.9121
B) 0.4099
C) 0.4494
D) 2.2251
E) 1.0963

Question 6

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side. k = 32.0 mi, l = 36.0 mi
The unknown side m is _____ mi.

A) 4.0
B) 16.5
C) 36.2
D) 48.2
E) 32.2

Question 7

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side. k = 30.2 mi, l = 41.1 mi
The unknown side m is _____ mi.

A) 51.0
B) 30.4
C) 27.9
D) 41.2
E) 71.3

Question 8

Find the angle rounded to the nearest hundredth of a degree. cos A = 0.7318

A) A = 42.96 ^o
B) A = 53.80 ^o
C) A = 85.75 ^o
D) A = 47.04 ^o
E) A = 77.01 ^o

Question 9

Use the triangle in the illustration. Find tan L rounded to three significant digits.

A) 0.141
B) 0.069
C) 0.691
D) 0.951
E) 0.447

Question 10

Find the angle rounded to the nearest tenth of a degree. tan B = 0.8081

A) B = 38.9 ^o
B) B = 55.9 ^o
C) B = 36.1 ^o
D) B = 39.6 ^o
E) B = 60.0 ^o

Question 11

Use the triangle in the illustration. Find cos K rounded to three significant digits.

A) 29.0
B) 0.626
C) 0.14
D) 0.779
E) 6.26

Question 12

Find the angle rounded to the nearest tenth of a degree. cos C = 0.8510

A) C = 49.6 ^o
B) C = 58.3 ^o
C) C = 37.8 ^o
D) C = 31.7 ^o
E) C = 65.4 ^o

Question 13

Find the value of the trigonometric ratio rounded to four significant digits. cos 51.7 ^o

A) 1.2662
B) 0.7848
C) 1.2742
D) 0.6198
E) 0.7898

Question 14

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side. a = 1.29 km, b = 4.12 km
The unknown side c is _____ km.

A) 4.31
B) 4.46
C) 1.61
D) 5.41
E) 3.91

Question 15

The angle adjacent to side e is _____.

A) ∠D
B) ∠F
C) ∠E

Question 16

Find the value of the trigonometric ratio rounded to four significant digits. tan 80.55 ^o

A) 6.008
B) 0.1642
C) 0.9864
D) 0.1664
E) 6.091

Question 17

Find the angle rounded to the nearest tenth of a degree. tan C = 0.8660

A) C = 40.9 ^o
B) C = 30.0 ^o
C) C = 75.2 ^o
D) C = 60.0 ^o
E) C = 88.4 ^o

Question 18

Find the angle rounded to the nearest tenth of a degree. sin B = 0.3290

A) B = 19.2 ^o
B) B = 18.2 ^o
C) B = 72.8 ^o
D) B = 19.6 ^o
E) B = 54.2 ^o

Question 19

Find the angle rounded to the nearest hundredth of a degree. sin A = 0.9382

A) A = 69.75 ^o
B) A = 71.04 ^o
C) A = 46.83 ^o
D) A = 96.91 ^o
E) A = 20.25 ^o

Question 20

The hypotenuse is _____.

A) a
B) c
C) b

Question 21

Find the angle rounded to the nearest tenth of a degree.
sin A = 0.2555
A = __________ ^o

Question 22

Using the triangle in the illustration, find tan A, rounded to three significant digits. tan A = __________

Question 23

Find the value of the trigonometric ratio rounded to three significant digits.
tan 77.05° = __________

Question 24

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side.
k = 20.2 mi, l = 16.1 mi Side m is __________ mi.

Question 25

Find the angle rounded to the nearest hundredth of a degree.
sin B = 0.2724
B = __________ ^o

Question 26

Find the angle rounded to the nearest tenth of a degree.
tan C = 0.1553
C = __________ ^o

Question 27

Using the triangle in the illustration, find cos K. cos K = __________

Question 28

Find the angle rounded to the nearest tenth of a degree.
tan C = 3.3873
Angle C = __________ ^o

Question 29

The angle opposite side d is __________.

Question 30

Find the value of the trigonometric ratio rounded to four significant digits.
sin 38.72° = __________

Question 31

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side.
k = 23.0 mi, l = 40.0 mi Side m is __________ mi.

Question 32

Find the value of the trigonometric ratio rounded to four significant digits.
sin 48.3° = __________

Question 33

The angle adjacent to side l is __________.

Question 34

Find the value of the trigonometric ratio rounded to four significant digits.
cos 53.1° = __________

Question 35

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side, rounded to two significant digits.
a = 2.91 km, b = 3.62 km Side c is __________ km.

Question 36

Use the right triangle in the illustration and the Pythagorean theorem to find the unknown side.
a = 49,200 m, b = 44,900 m Side c is __________ m.

Question 37

Find the angle rounded to the nearest tenth of a degree.
cos A = 0.7376
A = __________ ^o

Question 38

A conveyor is used to lift paper to a shredder. The most efficient operating angle of elevation for the conveyor is 37.6 ^o. The paper is to be elevated 12.0 m. What length of conveyor is needed? Round your answer to the appropriate number of significant digits.

A) 15.1 m
B) 9.5 m
C) 19.7 m
D) 15.6 m
E) 7.3 m

Question 39

Find the angle rounded to the nearest hundredth of a degree.
cos B = 0.7852
B = __________ ^o

Question 40

Find the value of the trigonometric ratio rounded to four significant digits.
tan 13.75° = __________

Question 41

A roadbed rises 250 ft for each 2800 ft of horizontal. (See the illustration.) Find the angle of inclination of the roadbed. (This is usually referred to as % of grade.) Round your answer to the appropriate number of significant digits.

A) 7.8 ^o
B) 5.1 ^o
C) 6.7 ^o
D) 6.4 ^o
E) 6.2 ^o

Question 42

A small plane takes off from an airport and begins to climb at a 15.0 ^o angle of elevation at $50 \overline { 0 }$ ft/min. After 25.0 min, how far along the ground will the plane have flown? Round your answer to the appropriate number of significant digits.

A) 12,800 ft
B) 12,400 ft
C) 12,300 ft
D) 12,700 ft
E) 12,100 ft

Question 43

Machinists often use a coordinate system to drill holes by placing the origin at the most convenient location. A bolt circle is the circle formed by completing an arc through the centers of the bolt holes in a piece of metal. Find the coordinates of the centers of points A, D, and G for the equally spaced $\frac { 1 } { 3 }$ -in. holes on a bolt circle of radius 7.00 in., as shown in the illustration. Round your answer to the nearest tenth.

A) A = (-4.9, 0.0) D = (7.0, 4.9) G = (0.0, -7.0)
B) A = (7.0, 0.0) D = (-4.9, -7.0) G = (0.0, 0.0)
C) A = (7.0, 0.0) D = (-4.9, 4.9) G = (0.0, -7.0)
D) A = (7.0, -7.0) D = (-4.9, 4.9) G = (0.0, 0.0)

Question 44

Find length x and angle A in the illustration. Round your answer to the appropriate number of significant digits.

A) $\angle A = 54.6 ^ { \circ } , 24.2 \mathrm { ft }$
B) $\angle A = 56.3 ^ { \circ } , 23.1 \mathrm { ft }$
C) $\angle A = 53.5 ^ { \circ } , 24.8 \mathrm { ft }$
D) $\angle A = 54.3 ^ { \circ } , 23.9 \mathrm { ft }$
E) $\angle A = 55.2 ^ { \circ } , 25.9 \mathrm { ft }$

Question 45

Enrico has to draft a triangular roof to a house. (See the illustration.) The roof is 30 ft wide. If the rafters are 26 ft long, at what angle will the rafters be laid at the eaves? Assume no overhang. Round your answer to the appropriate number of significant digits.

A) 55.4 ^o
B) 57.9 ^o
C) 57.5 ^o
D) 54.8 ^o
E) 55.9 ^o

Question 46

A bullet is found embedded in the wall of a room 2.3 m above the floor. The bullet entered the wall going upward at an angle of 14 ^o. How far from the wall was the bullet fired if the gun was held 1.2 m above the wall? Round your answer to the appropriate number of significant digits.

A) 5.5 m
B) 4.4 m
C) 6.1 m
D) 0.3 m
E) 3.8 m

Question 47

A railroad track has an angle of elevation of 7.0 ^o. What is the difference in height (in feet) of two points on the track 1.00 mi apart? Round your answer to the appropriate number of significant digits.

A) 651 ft
B) 665 ft
C) 664 ft
D) 648 ft
E) 669 ft

Question 48

A conveyor is used to lift paper to a shredder. The most efficient operating angle of elevation for the conveyor is 35.9°. The paper is to be elevated 11.0 m. What length of conveyor is needed? Round your answer to the appropriate number of significant digits.
length of conveyor = __________ meters

Question 49

Round metal duct runs along side some stairs from the floor to the ceiling. If the ceiling is 8.00 ft high and the angle of elevation between the floor and duct is 36.0 ^o, how long is the duct? Round your answer to the appropriate number of significant digits.

A) 13.6 ft
B) 12.0 ft
C) 12.5 ft
D) 12.7 ft
E) 15.3 ft

Question 50

Find length AB along the roofline of the building in the illustration. The slope of the roof is 49.0 ^o. Round your answer to the appropriate number of significant digits.

A) 25.0 ft
B) 24.4 ft
C) 26.1 ft
D) 25.5 ft
E) 26.4 ft

Question 51

In ac (alternating current) circuits, the relationship between the impedance Z (in ohms), the resistance R (in ohms), the phase angle $\theta$ , and the reactance X (in ohms) is shown by the right triangle in the illustration.
a. Find the impedance if the resistance is 380 ? and the phase angle is 23 ^o. Round your answer to the appropriate number of significant digits.
b. Suppose the resistance is 520 ? and the impedance is $7 \overline { 0 } 0$ ? . What is the phase angle? Round your answer to the appropriate number of significant digits.
c. Suppose the reactance is 190 ? and the resistance is 220 ? . Find the impedance and the phase angle. Round your answers to the appropriate number of significant digits.

A) a. 410 ? , b. 42 ^o, c. 290 ? , 41 ^o
B) a. 330 ? , b. 41 ^o, c. 330 ? , 36 ^o
C) a. 700 ? , b. 42 ^o, c. 290 ? , 42 ^o
D) a. 700 ? , b. 41 ^o, c. 410 ? , 23 ^o
E) a. 290 ? , b. 23 ^o, c. 410 ? , 41 ^o

Question 52

The cables attached to a TV relay tower are $13 \overline { 0 }$ m long. They meet level ground at an angle of 50 ^o, as in the illustration. Find the height of the tower. Round your answer to the appropriate number of significant digits.

A) 99.6 m
B) 96.9 m
C) 98.0 m
D) 100.0 m
E) 98.5 m

Question 53

A benchmark has been covered up with dirt and needs to be found. The CAD drawing shows it is located 37.0.0-feet from a property stake at an angle of $$1130 ^ { \circ }$$ What distance "B" from the stake parallel to the curb line should you start to dig to find this benchmark? Round your answer to the appropriate number of significant digits.

A) 30.1 ft
B) 29.0 ft
C) 32.8 ft
D) 34.1 ft
E) 37.3 ft

Question 54

The recommended safety angle of a ladder against a building is 71 ^o. A $1 \overline { 0 }$ -m ladder will be used. How high up on the side of the building will the ladder safely reach? (See the illustration.) Round your answer to the appropriate number of significant digits.

A) 11 m
B) 9.5 m
C) 8.9 m
D) 7.8 m
E) 8.4 m

Question 55

A piece of conduit 39.0 ft long cuts across the corner of a room, as shown in the illustration. Find length x and angle A. Round each answer to the appropriate number of significant digits.

A) $\angle A =$ 59.7°, x = 34.7 ft
B) $\angle A =$ 61.4°, x = 33.0 ft
C) $\angle A =$ 60.8°, x = 34.1 ft
D) $\angle A =$ 58.6°, x = 31.9 ft
E) $\angle A =$ 59.1°, x = 32.4 ft

Question 56

A mechanical draftsperson needs to find the distance across the corners of a hex-bolt. See the illustration. If the distance across the flats is 3.96 cm, find the distance x across the corners. Round your answer to the appropriate number of significant digits.

A) 7.52 cm
B) 6.32 cm
C) 9.92 cm
D) 7.92 cm
E) 5.22 cm

Question 57

A smokestack is $19 \overline { 0 }$ ft high. A guy wire must be fastened to the stack 30.0 ft from the top. The guy wire makes an angle of 40.0 ^o with the ground. Find the length of the guy wire. Round your answer to the appropriate number of significant digits.

A) 270 ft
B) 249 ft
C) 276 ft
D) 261 ft
E) 255 ft

Question 58

Find the width of the river in the illustration. Round your answer to the appropriate number of significant digits.

A) 113 m
B) 108 m
C) 105 m
D) 115 m
E) 112 m

Question 59

Twelve equally spaced holes must be drilled on a 13.700-in.-diameter bolt circle. (See the illustration.) What is the straight-line center-to-center distance between two adjacent holes? Round your answer to the appropriate number of significant digits.

A) 4.3458 in.
B) 3.5458 in.
C) 4.1458 in.
D) 5.5458 in.
E) 0.8458 in.

Question 60

From the base of a building, measure out a horizontal distance of 225 ft along the ground. The angle of elevation to the top of the building is 57.0 ^o. Find the height of the building.

A) 338 ft
B) 362 ft
C) 366 ft
D) 346 ft
E) 319 ft

Question 61

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 61.0 cm, c = 122 cm

A) A = 81.0 ^o, B = 9.0 ^o
B) A = 25.0 ^o, B = 65.0 ^o
C) A = 45.0 ^o, B = 45.0 ^o
D) A = 40.0 ^o, B = 50.0 ^o
E) A = 30.0 ^o, B = 60.0 ^o

Question 62

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 827 km, b = 2,770 km

A) A = 19.1 ^o, B = 70.9 ^o
B) A = 11.6 ^o, B = 78.4 ^o
C) A = 16.6 ^o, B = 73.4 ^o
D) A = 20.4 ^o, B = 69.6 ^o
E) A = 36.2 ^o, B = 53.8 ^o

Question 63

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 0.6211 cm, c = 0.7937 cm

A) A = 17.25 ^o, B = 72.75 ^o
B) A = 35.77 ^o, B = 54.23 ^o
C) A = 48.99 ^o, B = 41.01 ^o
D) A = 56.49 ^o, B = 33.51 ^o
E) A = 51.49 ^o, B = 38.51 ^o

Question 64

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 24.54 ft, c = 41.38 ft

A) A = 36.37 ^o, B = 53.63 ^o
B) A = 38.87 ^o, B = 51.13 ^o
C) A = 41.37 ^o, B = 48.63 ^o
D) A = 19.30 ^o, B = 70.70 ^o
E) A = 31.87 ^o, B = 58.13 ^o

Question 65

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 20.72 m, c = 46.92 m

A) A = 17.85 ^o, B = 72.15 ^o
B) A = 31.21 ^o, B = 58.79 ^o
C) A = 23.71 ^o, B = 66.29 ^o
D) A = 63.79 ^o, B = 26.21 ^o
E) A = 36.62 ^o, B = 53.38 ^o

Question 66

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 2,420 km, c = 3,580 km

A) A = 20.01 ^o, B = 69.99 ^o
B) A = 40.03 ^o, B = 49.97 ^o
C) A = 31.72 ^o, B = 58.28 ^o
D) A = 47.47 ^o, B = 42.53 ^o
E) A = 47.53 ^o, B = 42.47 ^o

Question 67

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 1,415 km, b = 2,982 km

A) A = 25.38 ^o, B = 64.62 ^o
B) A = 69.62 ^o, B = 20.38 ^o
C) A = 35.81 ^o, B = 54.19 ^o
D) A = 62.12 ^o, B = 27.88 ^o
E) A = 20.80 ^o, B = 69.20 ^o

Question 68

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 15.2 m, c = 84.3 m

A) A = 10.4 ^o, B = 79.6 ^o
B) A =32.2 ^o, B = 57.8 ^o
C) A =19.5 ^o, B = 70.5 ^o
D) A =7.9 ^o, B = 82.1 ^o
E) A =15.4 ^o, B = 74.6 ^o

Question 69

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 836 m, b = 192 m

A) A = 53.3 ^o, B = 36.7 ^o
B) A = 74.6 ^o, B = 15.4 ^o
C) A = 82.1 ^o, B = 7.9 ^o
D) A = 77.1 ^o, B = 12.9 ^o
E) A = 72.9 ^o, B = 17.1 ^o

Question 70

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 1,227 ft, c = 1,378 ft

A) A = 65.43 ^o, B = 24.57 ^o
B) A = 30.57 ^o, B = 59.43 ^o
C) A = 18.91 ^o, B = 71.09 ^o
D) A = 27.07 ^o, B = 62.93 ^o
E) A = 57.93 ^o, B = 32.07 ^o

Question 71

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 14.6 m, c = 16.1 m

A) A = 20.8 ^o, B = 69.2 ^o
B) A = 24.9 ^o, B = 65.1 ^o
C) A = 67.6 ^o, B = 22.4 ^o
D) A = 16.4 ^o, B = 73.6 ^o
E) A = 70.1 ^o, B = 19.9 ^o

Question 72

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 8,897 km, c = 9,814 km

A) A = 65.03 ^o, B = 24.97 ^o
B) A = 62.53 ^o, B = 27.47 ^o
C) A = 56.93 ^o, B = 33.07 ^o
D) A = 70.03 ^o, B = 19.97 ^o
E) A = 70.68 ^o, B = 19.32 ^o

Question 73

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 45.8 cm, c = 58.5 cm

A) A = 72.6 ^o, B = 17.4 ^o
B) A = 56.5 ^o, B = 33.5 ^o
C) A = 59.8 ^o, B = 30.2 ^o
D) A = 49.0 ^o, B = 41.0 ^o
E) A = 51.5 ^o, B = 38.5 ^o

Question 74

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 151 km, b = 674 km

A) A = 12.6 ^o, B = 77.4 ^o
B) A = 26.0 ^o, B = 64.0 ^o
C) A = 32.0 ^o, B = 58.0 ^o
D) A = 15.1 ^o, B = 74.9 ^o
E) A = 17.6 ^o, B = 72.4 ^o

Question 75

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 57.06 mi, b = 97.82 mi

A) A = 30.26 ^o, B = 59.74 ^o
B) A = 20.61 ^o, B = 69.39 ^o
C) A = 25.26 ^o, B = 64.74 ^o
D) A = 32.76 ^o, B = 57.24 ^o
E) A = 32.77 ^o, B = 57.23 ^o

Question 76

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 4.398 m, c = 5.821 m

A) A = 51.57 ^o, B = 38.43 ^o
B) A = 54.07 ^o, B = 35.93 ^o
C) A = 40.93 ^o, B = 49.07 ^o
D) A = 21.20 ^o, B = 68.80 ^o
E) A = 32.77 ^o, B = 57.23 ^o

Question 77

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 348.2 m, b = 495.2 m

A) A = 30.11 ^o, B = 59.89 ^o
B) A = 20.71 ^o, B = 69.29 ^o
C) A = 35.11 ^o, B = 54.89 ^o
D) A = 31.67 ^o, B = 58.33 ^o
E) A = 32.61 ^o, B = 57.39 ^o

Question 78

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 35.1 mm, b = 60.7 mm, c = 70.2 mm

A) A = 43.3 ^o, B = 46.7 ^o
B) A = 15.0 ^o, B = 75.0 ^o
C) A = 30.0 ^o, B = 60.0 ^o
D) A = 45.0 ^o, B = 45.0 ^o
E) A = 26.9 ^o, B = 63.1 ^o

Question 79

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. a = 243.2 km, b = 272.1 km

A) A = 46.79 ^o, B = 43.21 ^o
B) A = 44.29 ^o, B = 45.71 ^o
C) A = 31.82 ^o, B = 58.18 ^o
D) A = 41.79 ^o, B = 48.21 ^o
E) A = 19.16 ^o, B = 70.84 ^o

Question 80

Using the illustration, find the measure of each acute angle for the right triangle below. Answers are rounded using the appropriate rule for significant digits. b = 422 km, c = 621 km

A) A = 47.2 ^o, B = 42.8 ^o
B) A = 44.7 ^o, B = 45.3 ^o
C) A = 71.6 ^o, B = 18.4 ^o
D) A = 73.3 ^o, B = 16.7 ^o
E) A = 37.8 ^o, B = 52.2 ^o