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Name: ______________________ Class: _________________ Date: _________ ID: A Directions for all problems on this test: Round your decimals to three decimal places. You must show your work. Attach all work to the back of the test when you turn it in. Trig Test #2 Review: Non-right triangle trig 1. Given triangle ABC with a = 3, A = 40°, and B = 27°, find c. 2. Solve triangle ABC given that A = 47°, B = 52°, and b = 78. 3. Given triangle ABC with a = 10, b = 13, and A = 19°, find c. 4. Find the area of ΔABC. The figure is not drawn to scale. 5. Find the area of ΔABC. The figure is not drawn to scale. 6. Make up an example for which the law of sines will not work and explain why it will not work. Include a drawing to illustrate your example. 7. Solve ΔABC with A = 33°, a = 6.5, and b = 3. 8. Solve ΔABC with A = 110°, a = 5, and b = 7.3. 9. Given triangle ABC with b = 8, c = 5, and A = 58°, find a. 1 Name: ______________________ ID: A 10. Solve triangle ABC given that a = 19, b = 10, and c = 14. A 50-foot ramp makes an angle of 4.9° with the horizontal. To meet new accessibility guidelines, a new ramp must be built so it makes an angle of 2.7° with the horizontal. 11. What will be the length of the new ramp? The roof of a house is being reconstructed to accommodate heavy snows. The current 32-foot roofline makes an 18.2° angle with the horizontal. The owner has decided to construct the new roof so that it makes a 50° angle with the horizontal. 12. What will be the length of the new roofline? 13. How much higher will the new roof be? 14. Find the area of ΔABC . 2 Name: ______________________ ID: A 15. Use Trigonometry to investigate the lengths of the diagonals of the isosceles trapezoid with bases 4 centimeters and 7 centimeters long and a height of 6 centimeters. Find XY Find AX Find AB Find cos A Find BD. 16. Explain when it is appropriate to use the law of sines and when it is appropriate to use the law of cosines to solve a triangle. Solve ΔABC. 17. Find the area of ΔABC. 18. 3 Name: ______________________ ID: A 19. 20. Ships Two ships leave Boston Harbor at the same time. What is the distance between ships A and C after they have traveled 80 kilometers and 70 kilometers respectively? 21. Ravine Width Use the diagram to find the distance across the ravine. 4 ID: A Trig Test #2 Review: Non-right triangle trig Answer Section 1. ANS: 4.30 PTS: 1 DIF: Level B REF: MAL21754 TOP: Lesson 13.5 Apply the Law of Sines KEY: triangle | trigonometry | Law of Sines BLM: Comprehension NOT: 978-0-618-65615-8 2. ANS: C = 81°, a = 72.39, c = 97.76 PTS: 1 DIF: Level B REF: MAL21756 TOP: Lesson 13.5 Apply the Law of Sines KEY: solve | triangle | Law of Sines BLM: Comprehension NOT: 978-0-618-65615-8 3. ANS: c = 21.35 or 3.23 PTS: 1 DIF: Level B REF: MAL21764 TOP: Lesson 13.5 Apply the Law of Sines KEY: triangle | trigonometry | Law of Sines BLM: Comprehension NOT: 978-0-618-65615-8 4. ANS: 2 31.41 cm PTS: 1 DIF: Level B REF: MAL21767 TOP: Lesson 13.5 Apply the Law of Sines KEY: acute | triangle | trigonometry | sine | SAS | area BLM: Comprehension NOT: 978-0-618-65615-8 5. ANS: 2 14.67 cm PTS: 1 DIF: Level B REF: MAL21768 TOP: Lesson 13.5 Apply the Law of Sines KEY: area | acute | triangle | trigonometry | sine | SAS BLM: Comprehension NOT: 978-0-618-65615-8 6. ANS: Sample answer: Let m∠A = 40°, b = 20 inches, and a = 5 inches. Using the law of sines, 5 20 20 sin 40° = and thus sin B = , or sin B = 4 sin 40°. But sin B ≠ 4 sin 40° since 4 sin 40°>1. sin 40° sin B 5 (When trying to construct the triangle, side BC is too short to form a triangle.) PTS: 1 DIF: Level C REF: MAL21774 NAT: NCTM 9-12.GEO.1.c TOP: Lesson 13.5 Apply the Law of Sines KEY: Law of Sines BLM: Comprehension NOT: 978-0-618-65615-8 1 ID: A 7. ANS: In ΔABC B ≈ 14.6°, C ≈ 132.4°, and c ≈ 8.8. PTS: 1 DIF: Level B REF: A2.13.05.FR.10 TOP: Lesson 13.5 Apply the Law of Sines KEY: Free response | law of sines | acute angle | SSA BLM: Comprehension NOT: 978-0-618-65615-8 8. ANS: No solution. It is not possible to draw the indicated triangle. PTS: 1 DIF: Level B REF: A2.13.05.FR.11 TOP: Lesson 13.5 Apply the Law of Sines KEY: Free response | law of sines | SSA BLM: Comprehension NOT: 978-0-618-65615-8 9. ANS: 6.83 PTS: 1 DIF: Level B REF: MAL21775 TOP: Lesson 13.6 Apply the Law of Cosines KEY: triangle | Law of Cosines | side BLM: Comprehension NOT: 978-0-618-65615-8 10. ANS: A = 103.4°, B = 30.8°, C = 45.8° PTS: 1 DIF: Level B REF: MAL21779 TOP: Lesson 13.6 Apply the Law of Cosines KEY: triangle | Law of Sines | Law of Cosines BLM: Comprehension NOT: 978-0-618-65615-8 11. ANS: ≈90.66 ft PTS: 1 DIF: Level B REF: MAL21782 TOP: Lesson 13.6 Apply the Law of Cosines KEY: Law of Sines BLM: Application NOT: 978-0-618-65615-8 12. ANS: ≈47.29 ft PTS: 1 DIF: Level B REF: MAL21783 TOP: Lesson 13.6 Apply the Law of Cosines KEY: Law of Cosines BLM: Application NOT: 978-0-618-65615-8 13. ANS: ≈26.23 ft PTS: 1 DIF: Level B REF: MAL21784 TOP: Lesson 13.6 Apply the Law of Cosines KEY: Law of Cosines BLM: Application NOT: 978-0-618-65615-8 2 ID: A 14. ANS: 276.96 PTS: 1 DIF: Level B REF: MAL21785 TOP: Lesson 13.6 Apply the Law of Cosines KEY: area | heron | triangle BLM: Comprehension NOT: 978-0-618-65615-8 15. ANS: XY = 4 cm; AX = 1.5 cm; AB = 38.25 cm (or 6.18 cm); cos A = 0.24; 2 2 2 BD = AB + AD − 2 ⋅ AB ⋅ AD ⋅ cos A = 38.25 + 49 – 2( 38.25 )(7)(0.24) = 66.49 cm so BD = 66.49 cm ≈ 8.15 cm PTS: 1 DIF: Level C REF: MAL21788 TOP: Lesson 13.6 Apply the Law of Cosines KEY: Law of Cosines | trapezoid | diagonal BLM: Application NOT: 978-0-618-65615-8 16. ANS: Sample answer: Use the law of sines when given the measures of two angles and the length of one side of a triangle. Use the law of cosines when given the lengths of two sides and the measure of their included angle, or when given the measures of all three sides. PTS: 1 DIF: Level C REF: MAL21789 NAT: NCTM 9-12.COM.2 STA: GA.GPS.MTH.04.6-12.M6P1.d | GA.GPS.MTH.04.6-12.M6P3.a | GA.GPS.MTH.04.6-12.M6P3.b TOP: Lesson 13.6 Apply the Law of Cosines BLM: Comprehension NOT: 978-0-618-65615-8 17. ANS: C = 145°, a ≈ 4.5, b ≈ 5.9 PTS: 1 DIF: Level B TOP: Ch. 13 Test, Level A BLM: Comprehension 18. ANS: 34.6 REF: A2.13.TestA.Eng.19 KEY: Pre-made Test | Law of Sines NOT: 978-0-618-65615-8 PTS: 1 DIF: Level B TOP: Ch. 13 Test, Level A BLM: Comprehension 19. ANS: 158.7 REF: A2.13.TestA.Eng.22 KEY: Pre-made Test | area NOT: 978-0-618-65615-8 PTS: 1 DIF: Level B TOP: Ch. 13 Test, Level A BLM: Comprehension REF: A2.13.TestA.Eng.23 KEY: Pre-made Test | area NOT: 978-0-618-65615-8 3 ID: A 20. ANS: 101.6 PTS: 1 DIF: Level B REF: A2.13.TestB.Eng.25 TOP: Ch. 13 Test, Level B KEY: Pre-made Test | indirect measurement BLM: Application NOT: 978-0-618-65615-8 21. ANS: 37 m PTS: 1 DIF: Level C REF: A2.13.TestC.Eng.25 TOP: Ch. 13 Test, Level C KEY: Pre-made Test | indirect measurement BLM: Application NOT: 978-0-618-65615-8 4