Class Date Practice Form G Trigonometry Write the ratios for sin X, cos X, and tan X 1 2 The sine, cosine, and tangent ratios each have a reciprocal ratio
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Name Class Date
Practice Form G
Trigonometry
Write the ratios for sin
X, cos X, and tan X.1. 2. 3.
Find the value of
x.Round to the nearest tenth.
4. 5.
6. 7.
8. An escalator at a shopping center is 200 ft 9 in. long, and rises at an
angle of 15°. What is the vertical rise of the escalator? Round to the nearest inch.9. A 12-ft-long ladder is leaning against a wall and makes a 77° angle
with the ground. How high does the ladder reach on the wall?Round to the nearest inch.
10. A straight ramp rises at an angle of 25.5°and has a base 30 ft long. How high is
the ramp? Round to the nearest foot.Find the value of
x. Round to the nearest degree.11. 12.
13. 14.
5 1213X Z Y 816
Y X Z 8 "3 812
X ZY "4 5 x 14 33
14 x 37
?5.4 x 29
33
x 55
2924
x? 20 9 x? 17 11 x?2912 x? 12 13 5 13 12 5 1 2 23
2 ; 23 3 15 3 2 3 15 2
7.611.2
3.047.1
51 ft 11 in., or 623 in.
11 ft 8 in., or 140 in.
14 ft 565763
22
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
15. ?e 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.16. ?e 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.
Find the values of
w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.17. 18.
19. Writing Explain why tan 45°=1.
?e sine, cosine, and tangent ratios each have a reciprocal ratio. ?e reciprocal ratios are cosecant (csc), secant (sec), and cotangent (cot). Use △DEF and the de?nitions below to write each ratio. csc X 1 sin X sec X= 1 cos X cot X= 1 tan X20. csc D 21. sec D 22. cot D
23. csc F 24. sec F 25. cot F
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 cot X cos X sin X is an identity.27. Reasoning Does sin A+sin B=sin (A+B) when 06A+B690?
Explain your reasoning.
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
29. A right triangle has an angle that measures 28. ?e leg opposite the 28° angle
measures 13. Find the length of the other leg and the hypotenuse. Round your answers to the nearest tenth. 5.5 xw 45?35? 65
w 32
?x? 1816
8 D EF