Trigonometry

1
Trigonometry
Sine and Cosine Ratios
Start
2
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

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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
4
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
5
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
6
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
7
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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
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
16
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
17
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
18
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
19
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
20
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
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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
22
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
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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
24
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
25
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27
Example 5 Solution
3,078 ft
600 ft
x
A
x 11.2
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28
Example 6 Solution
500 m
x m
A
23
x 195.4 m
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End
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Example 7 Solution
28 in
x
A
55 in
x 30.6 in
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End
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Example 8 Solution
Adjacent leg
cos A
hypotenuse
55 m
x 84.8 m
x
5 m
A
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End
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Example 9 Solution
A
10
x m
120 m
x 20.8 m
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End
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Example 10 Solution
A
58 yd
25
x yd
x 24.5 yd
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Example 11 Solution
A
30
2
60
1
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Example 12 Solution
30
2
60
A
1
sin 60 0.8660
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Example 13 Solution
45
1
45
1
A
sin 45 0.7071
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End
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Example 14 Solution
A
Adjacent leg
cos A
hypotenuse
30
2
60
1
cos 30 0.8660
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End
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Example 15 Solution
Adjacent leg
cos A
hypotenuse
30
2
60
A
1
cos 60 0.5000
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End
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Example 16 Solution
Adjacent leg
cos A
hypotenuse
45
1
45
A
1
cos 45 0.7071
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End
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Example 17 Solution
A
Opposite leg
tan A
Adjacent leg
30
2
60
1
tan 30 0.5774
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End
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Example 18 Solution
Opposite leg
tan A
Adjacent leg
30
2
60
A
1
tan 60 1.7321
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End
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Example 19 Solution
Opposite leg
tan A
Adjacent leg
45
1
45
1
A
tan 45 1
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End
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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
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End
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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
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End
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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
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End
45
The End
Tangent Ratio