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LESSON 7.7 Answers for the lesson “Solve Right Triangles” Skill Practice 20. To determine the measure of angle T using cosine, the ratio is adjacent over hypotenuse; 1. angles, sides 2. Use the Pythagorean Theorem if 15 5 mT. cos21 } you have two sides of the triangle. 17 Use a trigonometric ratio if you 21. 308 22. 48.68 have an angle measure and a side length. 24. 50.28 25. 458 26. 15.68 3. 33.78 4. 24.48 5. 74.18 27. 11.08 6. 27.08 7. 53.18 8. 54.38 30. tan21 is the function which is 9. B 10. mK 5 508, KL ø 5.1, ML ø 6.1 11. mN 5 258, NP ø 21.4, NQ ø 23.7 12. mT 5 338, RS ø 9.7, RT ø 17.9 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 23. 70.78 13. mA ø 36.98, mB ø 53.18, AC ø 15 14. mD ø 70.58, mF ø 19.58, EF ø 8.5 28. 35.98 29. B used to determine the measure of an angle given the proper ratio of sides. 31. 458; 608 32. a. 0 to 108 b. 898 c. 608 d. no } 33. 6 cm, 2 cm, 2Ï 10 cm, 908, about 18.48, about 71.68 Problem Solving 15. mG ø 298, m J ø 618, 34. about 38.78 16. mA 5 46.48, AB ø 7.2, 12 35. about 59.78; tan21 } ø 59.78 7 HJ ø 7.7 AC ø 5.0 36. no 17. mD ø 29.78, mE ø 60.38, ED ø 5.4 18. mH 5 60.18, GJ ø 9.4, JH ø 5.4 19. WX should have been used instead 7 5 368. of WY; sin21 } WX BC 37. tan21 }; the information AC needed to determine the measure of A is given. If you used the tangent ratio, this will make the answer more accurate since no rounding has occurred. Geometry Answer Transparencies for Checking Homework 219 38. a. about 1716 ft 40. Sample answer: You want to b. about 2986 ft c. About 1270 ft; subtract the two distances to find out how far the two hikers are from each other. 39. a. 41. a. 38.4 ft b. about 71.2 ft x (inches) 20 21 22 y (degrees) 28.8 27.6 26.6 x (inches) 23 24 25 y (degrees) 25.6 24.6 23.7 x (inches) 26 27 y (degrees) 22.9 22.2 c. about 48.7 ft d. about 57.48, about 38.08; neither; the sides are not the same, so the triangles are not congruent, and the angles are not the same, so the triangles are not similar. e. Tangent was used because the b. y 30 Degrees Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. know how tall your town’s water tower is. You are standing 40 feet away from the base of the tower and the angle of elevation is 608. How tall is the water tower? 42. Statements (Reasons) 20 1. nABC with altitude } CD (Given) 10 0 height and the distance along the ground form a tangent relationship for the angle of elevation. 0 20 21 22 23 24 25 26 27 28 x Inches CD CD and sin B 5 } 2. sin A 5 } a b (Definition of sine) c. Sample answer: The longer the rack, the closer to 208 the angle gets. 3. CD 5 b sin A and CD 5 a sin B (Multiplication Property of Equality) Geometry Answer Transparencies for Checking Homework 220 4. b sin A 5 a sin B (Substitution Property of Equality) sin A sin B 5} 5. } b a 4. about 18.9 ft; 1 8 . 9 (Division Property of Equality) Mixed Review of Problem Solving 1. a. about 13.0 m b. about 17.8 m c. about 4.8 m } 2. a. friend10 myou Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 85 5. a. 9Ï 3 . Sample answer: Use the Pythagorean Theorem with n AEC, since n ACD is } is bisected by isosceles, and AD E, } EC is the altitude and is therefore perpendicular to the base. b. About 10.98. Sample answer: rock b. Use the tangent ratio. Find the measure of ACE using the sine ratio, then find the measure of ACB because it is supplementary to ACE. The Law of Cosines allowed me to find AB and then I used the Law of Sines to find the measure of ABC. c. about 76.5 m 1.35 3. about 2.4 m; sin 348 5 } x Geometry Answer Transparencies for Checking Homework 221 5. c. Sample answer: Part (a): Since the hypotenuse is 18 and the given leg is half of that, the triangle must be a 308-608-908 triangle and therefore, the other } leg must be 9Ï 3 ; part (b): EB must equal 3x and since } } x 5 9Ï 3 , EB 5 27 Ï3 . Now you can use the inverse tangent function to determine the measure of ABC. 6. about 8.6 ft; about 11.0 ft 7. 658; 5 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 6 Geometry Answer Transparencies for Checking Homework 222