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Trigonometry

Sine and Cosine Ratios

Start

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

- Menu
- End
- Back

Oops

- Try again

Example 5 Solution

3,078 ft

600 ft

x

A

x 11.2

Menu

End

Example 6 Solution

500 m

x m

A

23

x 195.4 m

Menu

End

Example 7 Solution

28 in

x

A

55 in

x 30.6 in

Menu

End

Example 8 Solution

Adjacent leg

cos A

hypotenuse

55 m

x 84.8 m

x

5 m

A

Menu

End

Example 9 Solution

A

10

x m

120 m

x 20.8 m

Menu

End

Example 10 Solution

A

58 yd

25

x yd

x 24.5 yd

Menu

End

Example 11 Solution

A

30

2

60

1

Menu

End

Example 12 Solution

30

2

60

A

1

sin 60 0.8660

Menu

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

Menu

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

Menu

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

Menu

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

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