Deck 19: Right-Triangle Trigonometry

Question 1

If a = 4.23, b = 10.07, and c = 10.92, express sin B as a decimal to the nearest ten-thousandth.

A)2.5816
B)0.9222
C)0.3874
D)1.0844

Answer 1

B

Question 2

In right triangle ABC, with right angle C, side a = 9, b = 12, and c = 15, find the sin A
expressed as a fraction in lowest terms.

Answer 2

Question 3

If a = 9, b = 12, and c = 15, express sin A as a fraction in lowest terms.

Answer 3

D

Question 4

If a = 7, b = 11, and c = 13.04, express tan A as a decimal to the nearest ten-thousandth.

A)0.5368
B)1.5714
C)1.1855
D)0.6364

Question 5

Find sin A to the nearest ten-thousandth if a = 14.5, b = 7.8, and c = 16.5.

A)0.8788
B)0.8485
C)0.4727
D)1.8591

Question 6

If a = 7, b = 11, and c = 13.04, express sin A as a decimal to the nearest ten-thousandth.

A)1.5714
B)1.8629
C)0.5368
D)0.8436

Question 7

In right triangle ABC, with right angle C, side a = 4.5, b = 5.4, and c = 7, find the sin A.
Round answer to nearest ten-thousandth.

Question 8

If a = 4.23, b = 10.07, and c = 10.92, express tan A as a decimal to the nearest ten-thousandth.

A)2.5816
B)2.3806
C)0.4201
D)0.3874

Question 9

In right triangle ABC, with right angle C, side a = 3.5, b = 7.2, and c = 8, find the cos A.
Round answer to the nearest ten-thousandth.

Question 10

If a = 4.23, b = 10.07, and c = 10.92, express sin A as a decimal to the nearest ten-thousandth.

A)2.3806
B)0.4201
C)2.5816
D)0.3874

Question 11

Find tan A as a fraction in lowest terms if a = 9, b = 12, and c = 15.

Question 12

In right triangle ABC, with right angle C, side a = 12, b = 16, and c = 20, find the cos A
expressed as a fraction in lowest terms.

Question 13

Find cos A to the nearest ten-thousandth if a = 14.5, b = 7.8, and c = 16.5.

A)2.1154
B)0.8788
C)0.4727
D)1.1379

Question 14

If a = 4.23, b = 10.07, and c = 10.92, express tan B as a decimal to the nearest ten-thousandth.

A)2.3806
B)0.4201
C)0.3874
D)0.9222

Question 15

In right triangle ABC, with right angle C, side a = 12, b = 16, and c = 20, find the tan B
expressed as a fraction in lowest terms.

Question 16

In right triangle ABC, with right angle C, side a = 9, b = 12, and c = 15, find the tan B
expressed as a fraction in lowest terms.

Question 17

Find csc B to the nearest ten-thousandth if a = 14.5, b = 7.8, and c = 16.5.

A)1.1379
B)0.8788
C)2.1154
D)0.4727

Question 18

Find cos B to the nearest ten-thousandth if a = 14.5, b = 7.8, and c = 16.5.

A)1.8590
B)0.4727
C)0.8788
D)1.1379

Question 19

Find tan A to the nearest ten-thousandth if a = 14.5, b = 7.8, and c = 16.5.

A)1.8591
B)1.1379
C)0.5379
D)1.8590

Question 20

If a = 9, b = 12, and c = 15, express cos A as a fraction in lowest terms.

Question 21

Use a calculator to find sin 1.0327. Round to four significant digits.

Question 22

Use a calculator to find tan 0.6512 rounded to the nearest ten-thousandth.

A)0.7621
B)0.0114
C)87.9811
D)1.3122

Question 23

Use a calculator to find the tan 53°. Round to four significant digits.

Question 24

Find tan B and round to the nearest ten-thousandth if a = 12, b = 10, and c = 15.6.

A)0.6410
B)0.8333
C)1.200
D)0.7692

Question 25

Use a calculator to find cos 3.2° rounded to the nearest ten-thousandth.

A)1.0017
B)0.9984
C)-0.9983
D)1.0016

Question 26

Find sin 43.6° to the nearest ten-thousandth.

A)0.6896
B)0.9523
C)-0.3731
D)0.7242

Question 27

Use a calculator to find the sin 0.4751. Round to four significant digits.

Question 28

Use the definitions of the sine, cosine, and tangent functions to verify the property:

Question 29

Use a calculator to find cos 2.31 rounded to the nearest ten-thousandth.

A)-1.4843
B)0.9992
C)1.0008
D)-0.6737

Question 30

Find cos A and round to the nearest ten-thousandth if a = 12, b = 10, and c = 15.6.

A)0.7692
B)0.8333
C)0.6410
D)1.200

Question 31

Use a calculator to find tan 0.5842. Round to four significant digits.

Question 32

Use a calculator to find tan 1.4752. Round to four significant digits.

Question 33

Use a calculator to find cos 0.1250. Round to four significant digits.

Question 34

Use a calculator to find cos 31°. Round to four significant digits.

Question 35

Use a calculator to find cos 1.1843. Round to four significant digits.

Question 36

Find tan 1.4387 to the nearest ten-thousandth.

A)0.0251
B)7.5261
C)0.1359
D)0.8339

Question 37

Find sin A and round to the nearest ten-thousandth if a = 12, b = 10, and c = 15.6.

A)0.7692
B)0.6410
C)1.200
D)0.8333

Question 38

Use a calculator to find sin 0.9657. Round to four significant digits.

Question 39

Use a calculator to find sin 54° rounded to the nearest ten-thousandth.

A)0.8090
B)-1.7896
C)-0.5588
D)1.2361

Question 40

Use a calculator to find tan 1.0853. Round to four significant digits.

Question 41

Use a calculator to find sin 42°28' rounded to the nearest ten-thousandth.

A)-0.9985
B)0.6752
C)1.0015
D)1.4811

Question 42

Find tan 0.8564 rounded to the nearest ten-thousandth.

A)2.348
B)1.1531
C)0.8672
D)0.4265

Question 43

Find 8 if cos 8 = 0.6896 rounded to the nearest tenth of a degree.

A)34.6°
B)42.6°
C)0.8°
D)46.4°

Question 44

Find 8 to the nearest ten-thousandth of a radian if sin 8 = 0.8253.

Question 45

Determine the radian measure of 8 if sin 8 = 0.5546 rounded to the nearest ten-thousandth.

A)0.5064 rad
B)33.6832 rad
C)0.9829 rad
D)0.5879 rad

Question 46

Find 8 to the nearest ten-thousandth of a radian if cos 8 = 0.2894.

Question 47

Determine the degree measure of 8 if sin 8 = 0.7022 rounded to the nearest tenth.

A)35.1°
B)0.8°
C)45.4°
D)44.6°

Question 48

Determine the degree measure of 8 if tan 8 = 0.7022 rounded to the nearest tenth.

A)54.9°
B)35.1°
C)45.4°
D)0.6°

Question 49

Given that sin 40° = 0.6428, which angle has the cosine value of 0.6428?

A)140°
B)40°
C)130°
D)50°

Question 50

Determine the radian measure of 8 if tan 8 = 0.2646 rounded to the nearest ten-thousandth.

A)0.2587 rad
B)1.3121 rad
C)3.8659 rad
D)14.8208 rad

Question 51

Find the radian measure of 8 to the nearest ten-thousandth if tan 8 = 0.6254.

Question 52

Determine the degree measure of 8 if cos 8 = 0.7022 in degree, minute, second rounded to the nearest second.

A)45° 23' 46"
B)0° 47' 32"
C)45° 39' 62"
D)44° 36' 13"

Question 53

Find 8 to the nearest 0.1° if sin 8 = 0.9939.

Question 54

Find 8 to the nearest 0.1° if tan 8 = 0.2157.

Question 55

Determine the degree measure of 8 if tan 8 = 0.7022 rounded to the nearest tenth.

A)44.6°
B)45.4°
C)54.9°
D)35.1°

Question 56

Determine the degree measure of angle 8 if sin 8 = 0.7342, rounding to the nearest tenth of a degree.

A)0.8°
B)1.5°
C)47.2°
D)42.8°

Question 57

Find sin 25.5° rounded to the nearest ten-thousandth.

A)0.3591
B)2.7851
C)2.3228
D)0.4305

Question 58

Find 8 if tan 8 = 0.6896 rounded to the nearest tenth of a degree.

A)46.4°
B)42.6°
C)34.6°
D)55.4°

Question 59

Determine the degree measure of angle 8 if cos 8 = 0.9106, rounding to the nearest tenth of a degree.

A)24.4°
B)0.4°
C)65.6°
D)2.3°

Question 60

Find 8 to the nearest ten-thousandth of a radian if sin 8 = 0.5107.

Question 61

Find 8 to the nearest ten-thousandth of a radian if tan 8 = 1.0537.

Question 62

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find c if B = 30° and b = 16 cm.

Question 63

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find a if b = 8 dm and c = 12 dm.

Question 64

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find c if B = 60° and b = 12 cm.

Question 65

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find c if A = 69.5° and a = 12 m.

Question 66

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find c if a = 8 in. and b = 5.4 in.

Question 67

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find a if A = 48° and c = 14 m.

Question 68

Find 8 to the nearest ten-thousandth of a radian if cos 8 = 0.7685.

Question 69

Determine the degree measure of angle 8 if tan 8 = 2.734, rounding to the nearest tenth of a degree.

A)0.8°
B)1.2°
C)69.9°
D)20.1°

Question 70

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find a if A = 43° and c = 18 m.

Question 71

Find 8 to the nearest ten-thousandth of a radian if tan 8 = 2.6051.

Question 72

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find c if a = 9 in. and b = 7.2 in.

Question 73

In right triangle ABC with right angle C, find the indicated part. Round to the nearest 0.1°.
Find B if A = 74.5° and a = 14 m.

Question 74

In right triangle ABC with right angle C, find the indicated part. Round to the nearest 0.1°.
Find A if a = 10 m and c = 12 m.

Question 75

Use the sine function to find the indicated part of triangle ABC. Round to four significant digits. Find c if b = 15.4 m and B = 31°.

A)29.90 m
B)38.12 m
C)7.932 m
D)0.03344 m

Question 76

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find a if b = 9 dm and c = 14 dm.

Question 77

In right triangle ABC with right angle C, find the indicated part. Round to four significant digits. Find c if A = 74.5° and a = 14 m.

Question 78

In right triangle ABC with right angle C, find the indicated part. Round to nearest 0.1°.
Find B if A = 69.5° and a = 12 m.

Question 79

Determine the radian measure of angle 8 if tan 8 = 1.5043, rounding to the nearest ten-thousandth.

A)56.3856 rad
B)33.6144 rad
C)1.0161 rad
D)0.9841 rad

Question 80

In right triangle ABC with right angle C, find the indicated part. Round to the nearest 0.1°.
Find A if a = 7 m and c = 10 m.