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Trigonometry

Sine and Cosine Ratios

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Sine and Cosine Ratios

Example 12 Example 13 Example 14 Example

15 Example 16 Example 17 Example 18 Example

19 Example 20 Example 21 Example 22

- Example 1
- Example 2
- Example 3
- Example 4
- Example 5
- Example 6
- Example 7
- Example 8
- Example 9
- Example 10
- Example 11

1. Find each tangent. Round to four decimal

places.

Q

10

sin Q

Ex. 1

6

S

R

8

A

C

B

D

None of these

2. Find each tangent. Round to four decimal

places.

Q

10

Ex. 2

sin R

6

S

R

8

A

C

B

D

None of these

3. Find each tangent. Round to four decimal

places.

35

X

Y

Ex. 3

cos Z

12

37

Z

A

C

B

D

None of these

4. Find each tangent. Round to four decimal

places.

35

X

Y

Ex. 4

cos Y

12

37

Z

A

C

B

D

None of these

5. Solve for x. Round to the nearest tenth.

Ex. 5

3,078 ft

600 ft

Solution

x

A

C

11.2 ft

11.1 ft

12.0 ft

B

D

None of these

6. Solve for x. Round to the nearest tenth.

Ex. 6

500 m

Solution

x m

23

A

C

195.4 m

195.5 m

196.1 m

B

D

None of these

7. Solve for x. Round to the nearest tenth.

Ex. 7

28 in

x

Solution

55 in

A

C

29.9 in

30.6 in

30.5 in

B

D

None of these

8. Solve for x. Round to the nearest tenth.

Ex. 8

55m

Solution

x

5 m

A

C

88.3 m

84.6 m

84.8 m

B

D

None of these

9. Solve for x. Round to the nearest tenth.

Ex. 9

10

Solution

x m

120 m

A

C

20.8 m

20.7 m

21.1 m

B

D

None of these

10. Solve for x. Round to the nearest tenth.

58 yd

25

Ex. 10

Solution

x yd

A

C

24.6 yd

24.5 yd

23.9 yd

B

D

None of these

11. Find each value. Round to four decimal places.

Ex. 11

30

2

sin 30 ?

Solution

60

1

A

C

0.5000

0.7071

0.8660

B

D

None of these

12. Find each value. Round to four decimal places.

Ex. 12

30

2

sin 60 ?

Solution

60

1

A

C

0.5774

0.7071

0.8660

B

D

None of these

13. Find each value. Round to four decimal places.

Ex. 13

45

1

sin 45 ?

Solution

45

1

A

C

0.5774

0.7071

0.8660

B

D

None of these

14. Find each value. Round to four decimal places.

Ex. 14

30

2

cos 30 ?

Solution

60

1

A

C

0.5774

0.7071

0.8660

B

D

None of these

15. Find each value. Round to four decimal places.

Ex. 15

30

2

cos 60 ?

Solution

60

1

A

C

0.5000

0.7071

0.8660

B

D

None of these

16. Find each value. Round to four decimal places.

Ex. 16

45

1

cos 45 ?

Solution

45

1

A

C

0.5774

0.7071

0.8660

B

D

None of these

17. Find each value. Round to four decimal places.

Ex. 17

30

2

tan 30 ?

Solution

60

1

A

C

0.8660

0.7071

0.5774

B

D

None of these

18. Find each value. Round to four decimal places.

Ex. 18

30

2

tan 60 ?

Solution

60

1

A

C

0.8660

1.7321

0.7071

B

D

None of these

19. Find each value. Round to four decimal places.

Ex. 19

45

1

tan 45 ?

Solution

45

1

A

C

0.8660

1

0.7071

B

D

None of these

20. If the hypotenuse of a right triangle is 5 ft

and measure of angle A equals 68, find the

measure of the leg adjacent to angle A.

A

Solution

5 ft

68

x

A

C

1.9 ft

2 ft

1.8 ft

B

D

None of these

21. In a right triangle the hypotenuse is 24

centimeters and the m Ð D 16. What is the

measure of the leg opposite Ð D.

24 cm

Solution

x

15

D

A

C

6.5 cm

5 cm

6.6 cm

B

D

None of these

22. To guard against a fall, a ladder should at

most make an angle of 75 with the ground. What

is the maximum height that a 20-foot ladder can

reach safely.

20 feet

Solution

x

75

D

A

C

19.3 feet

18 feet

19.4 feet

B

D

None of these

Correct

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Example 5 Solution

3,078 ft

600 ft

x

A

x 11.2

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End

Example 6 Solution

500 m

x m

A

23

x 195.4 m

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End

Example 7 Solution

28 in

x

A

55 in

x 30.6 in

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End

Example 8 Solution

Adjacent leg

cos A

hypotenuse

55 m

x 84.8 m

x

5 m

A

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End

Example 9 Solution

A

10

x m

120 m

x 20.8 m

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End

Example 10 Solution

A

58 yd

25

x yd

x 24.5 yd

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End

Example 11 Solution

A

30

2

60

1

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End

Example 12 Solution

30

2

60

A

1

sin 60 0.8660

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End

Example 13 Solution

45

1

45

1

A

sin 45 0.7071

Menu

End

Example 14 Solution

A

Adjacent leg

cos A

hypotenuse

30

2

60

1

cos 30 0.8660

Menu

End

Example 15 Solution

Adjacent leg

cos A

hypotenuse

30

2

60

A

1

cos 60 0.5000

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End

Example 16 Solution

Adjacent leg

cos A

hypotenuse

45

1

45

A

1

cos 45 0.7071

Menu

End

Example 17 Solution

A

Opposite leg

tan A

Adjacent leg

30

2

60

1

tan 30 0.5774

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End

Example 18 Solution

Opposite leg

tan A

Adjacent leg

30

2

60

A

1

tan 60 1.7321

Menu

End

Example 19 Solution

Opposite leg

tan A

Adjacent leg

45

1

45

1

A

tan 45 1

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End

Example 20 Solution If the hypotenuse of a

right triangle is 5 ft and measure of angle A

equals 68, find the measure of the leg adjacent

to angle A.

Adjacent leg

cos A

hypotenuse

x 1.9 ft

Menu

End

Example 21 SolutionIn a right triangle the

hypotenuse is 24 centimeters and the m Ð D 16.

What is the measure of the leg opposite Ð D.

Opposite leg

sin D

hypotenuse

24 cm

x

16

x 6.6 cm

D

Menu

End

Example 22 SolutionTo guard against a fall, a

ladder should at most make an angle of 75 with

the ground. What is the maximum height that a

20-foot ladder can reach safely.

Opposite leg

sin D

hypotenuse

20 feet

x

75

x 19.3 feet

D

Menu

End

The End

Tangent Ratio