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Name
Class
Date
Practice
8-3
Form G
Trigonometry
Write the ratios for sin X, cos X, and tan X.
X
1.
Y
2.
13
5
Y
8
Z
Z
12
12 5 12
13 ; 13 ; 5
X
3.
16
Y
X
8 63
1 "3 "3
2; 2 ; 3
7.6
14
33
x
3.0
6. x
Z
11.2
5.
14
x
4 65
"5 2 "5
3 ; 3; 2
Find the value of x. Round to the nearest tenth.
4.
12
8
37
47.1
7.
x
5.4
29
55
33
8. An escalator at a shopping center is 200 ft 9 in. long, and rises at an
angle of 158. What is the vertical rise of the escalator? Round to the
nearest inch. 51 ft 11 in., or 623 in.
9. A 12-ft-long ladder is leaning against a wall and makes a 778 angle
with the ground. How high does the ladder reach on the wall?
Round to the nearest inch. 11 ft 8 in., or 140 in.
10. A straight ramp rises at an angle of 25.58and has a base 30 ft long. How high is
the ramp? Round to the nearest foot. 14 ft
Find the value of x. Round to the nearest degree.
56
11.
29
63
12.
20
24
x
x
13.
9
57
17
14.
11
12
x
x
22
29
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
23
Name
Class
8-3
Date
Practice (continued)
Form G
Trigonometry
15. The lengths of the diagonals of a rhombus are 4 in. and 7 in. Find the measures
of the angles of the rhombus to the nearest degree. 59 and 121
16. The lengths of the diagonals of a rhombus are 5 in. and 8 in. Find the measures
of the angles of the rhombus to the nearest degree. 64 and 116
Find the values of w and then x. Round lengths to the nearest tenth and angle
measures to the nearest degree.
17.
18.
5
5.5
45
w
6
32
35
w
x
w 5 5.5; x 5 2.4
x
w 5 2.6; x 5 26
19. Writing Explain why tan 458 5 1. Answers may vary. Sample: The tangent of an
angle is the length of the opposite leg divided by the length of the adjacent side.
If the angle is 45°, then the opposite side and the adjacent sides are equal.
The sine, cosine, and tangent ratios each have a reciprocal ratio. The reciprocal
ratios are cosecant (csc), secant (sec), and cotangent (cot). Use kDEF and the
definitions below to write each ratio.
18
csc X 5 sin1 X
sec X 5 cos1 X
cot X 5 tan1 X
20. csc D 98
21. sec D 49
22. cot D 21
23. csc F 94
24. sec F 89
25. cot F 2
F
16
D 8 E
26. An identity is an equation that is true for all the allowed values of the variable.
Use what you know about trigonometric ratios to show that the equation
cos X
sin X
1
is an identity. cot X 5 tan1 X and tan X 5 cos
cot X 5
X , so tan X 5
sin X
1
sin X
cos X
5 cos X
sin X
27. Reasoning Does sin A 1 sin B 5 sin (A 1 B) when 0 , A 1 B , 90?
Explain your reasoning. No; answers may vary. Sample: sin 45 1 sin 30 5 0.707 1 0.5
and sin (40 1 35) 5 sin 75 5 .966.
28. A right triangle has a hypotenuse of length 10 and one leg of length 7. Find the
length of the other leg and the measures of the acute angles in the triangle.
Round your answers to the nearest tenth 7.1; 45.6; 44.4
29. A right triangle has an angle that measures 28. The leg opposite the 288 angle
measures 13. Find the length of the other leg and the hypotenuse. Round your
answers to the nearest tenth. 24.4; 27.7
Prentice Hall Gold Geometry • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
24