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Name _______________________________________ Date __________________ Class __________________ MODULE 13 Trigonometry with Right Triangles Module Quiz: B Use the figure for 1–2. 7. Are sin and cos reciprocals of each other? Explain. ________________________________________ ________________________________________ 8. Given that cos 42 0.743, what is the sine of the complementary angle? 1. Name the side opposite A. _______________________________________ ________________________________________ 2. Name the side adjacent to A. Use the figure for 9–10. _______________________________________ Use the figure for 3–5. 9. What is LK rounded to the nearest hundredth? Show your work. ________________________________________ State each of the following: ________________________________________ 3. What is tan D ? 10. What is JK rounded to the nearest hundredth? Show your work. _______________________________________ 4. What is sin D ? ________________________________________ ________________________________________ _______________________________________ 5. What is cos D ? Use the figure for 11–12. _______________________________________ A right triangle is shown. 11. What is m M ? ________________________________________ 6. If mH 68, what is GI? Show your work. ________________________________________ 12. What is mO? Explain how you got your answer. _______________________________________ ________________________________________ _______________________________________ ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 63 Name _______________________________________ Date __________________ Class _________________ MODULE 13 Trigonometry with Right Triangles Module Quiz: B PQR is shown. 17. What is the area of nearest tenth? VWX to the 13. What are the missing side lengths in PQR ? Explain. ________________________________________ _______________________________________ ________________________________________ _______________________________________ 18. Solve the triangle by finding the lengths of all the sides and the measures of all the angles. Show your reasoning. _______________________________________ TSU is shown. ________________________________________ 14. What are the missing side lengths in TSU? Explain. Keep your answer in simplified radical form. ________________________________________ ________________________________________ _______________________________________ 19. Find the side lengths to the nearest hundredth and the angle measures to the nearest degree. _______________________________________ 15. What is a Pythagorean Triple? _______________________________________ _______________________________________ 16. State whether the following are Pythagorean Triples or multiples of Pythagorean Triples. A 6, 8, 10 Yes No B 14, 48, 50 Yes No C 25, 25, 100 Yes No ________________________________________ ________________________________________ ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 64 Name _______________________________________ Date __________________ Class _________________ 5 so, 5.83 mF 59. Then mE 90 59 31. To find DF, 52 (DF)2 (5.83)2 or DF is about 2.998 ft. 18. To find mF , sin x MODULE 13 Trigonometry with Right Triangles Module Quiz 13: B 19. AB BC, so mB 90 AB 4, BC 8, 1. BC AC (4 ( 4))2 (4 8)2 80 8.9, 2. AB 3. 7 4 4. 7 8.1 5. 4 8.1 BC 8 mA tan1 tan1 63 AB 4 A and C are complementary, so mC 90 63 27. GI ; 2 tan 68 GI; GI 4.95 2 7.No; Sin of an angle is equal to the opposite side divided by the hypotenuse. Cosine of an angle is equal to the adjacent side divided by the hypotenuse. Both are divided by the hypotenuse so they are not reciprocals of each other. 8. 0.743 LK 9. sin 20 ; 8.5(sin 20) LK; LK 2.91 8.5 2.91 10. tan 20 ; JK(tan 20) 2.91; JK 8 JK 5 11. m M sin1 ; mM 27 11 6. tan 68 12. The sum of the interior angles of a triangle are 180, so mO 180 90 27 63. 13. In a 45-45-90 triangle, the hypotenuse is 2 times each leg. So, 12 QR 2 and QR 8.49. 14. TU 2 8 3 16 3; SU 3 8 3 8(3) 24 15. A Pythagorean triple is a set of 3 positive integers such that a2 b2 c2. 16. A Yes B Yes C No 17. A 1 4.17.2 sin 47 10.79 m2. 2 Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 65