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Name Class Date Practice 8-3 Form K Trigonometry Write the ratios for sin D, cos D, and tan D. 1. D 5 3 F 2. To start, write the ratio of sin D. Then determine the length of the side 9 /D and the length of the hypotenuse. opposite 4; 3; 4 5 5 3 z E 4 sin D 5 hypotenuse 15 D opposite 8 15 4 z u 5 E 3. 8 E 17 ; 17 ; 15 5 63 8 17 5 F F "3 ; 1 ; 2 2 10 5 "3 D Find the value of x. Round to the nearest tenth. To start, identify how the sides relate to the given angle. 4. Side x is 9 to the given angle. adjacent x 8 34 x 5. The given side is the hypotenuse. 6.6 6. 5.2 18.6 9 x 14 22 61 34.0 7. 20 8. 2.4 68 x x 36 6 9. The ramp on the back of a moving van is 3 ft high and rises at an angle of 258. How long is the ramp? Round to the nearest foot. 7 ft 10. A rope attached to the top of a tent is staked into the ground. The rope is 4.5 ft long. The angle formed by the rope and the ground is 468. How far from the center of the base of the tent is the rope staked? Round to the nearest tenth of a foot. 3.1 ft Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 25 Name Class Date Practice (continued) 8-3 Form K Trigonometry Find the value of x. Round to the nearest degree. To start, identify the given sides in relation to x. 11. Then write the trigonometric ratio. 3 The given sides are the side opposite x 10 17 /x 5 3 and the side adjacent to /x 5 u 10 . u tan x8 5 12. 3 u 10 u 13. 64 9 10 24 11 x 12 x 14. x 18 71 81 10 15. 1.6 x 17 Find the values of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree. 20.8; 62 17. 16. 30 w 5.8; 12.6 45 16 x 44 41 70 x w 18. Jed is building a roof for his shed. The highest point of the roof will be 3 ft higher than the top of the shed. The slanted roof will be 7 ft long. What is the measure of the angle formed by the top of the shed and the slanted roof? 258 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. csc X 5 sin1 X 17 19. csc D 8 D 17 sec X 5 cos1 X cot X 5 tan1 X 17 20. sec D 15 21. cot D 8 15 Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 26 E 8 15 F