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Name Class Date Extra Practice Chapter 14 Lesson 14-1 Simplify each trigonometric expression. 1. tan2 u 2 sec2 u 21 2. sin u sec u tanu csc u 4. sec u cot u 5. 1 1 tan2 u 1 1 cot2 u tan2 u 3. tan u cos u sin u 6. sin u(sec2 u 2 tan2 u) csc u sin2 u 1 Lesson 14-2 Use a unit circle and 30°-60°-90° triangles to find the degree measures of each angle. !3 7. angles whose sine is 2 60° 1 n · 360° and 120° 1 n · 360° 1 8. angles whose cosine is 22 120° 1 n · 360° and 240° 1 n · 360° 9. angles whose tangent is !3 60° 1 n · 360° and 240° 1 n · 360° Use a calculator and inverse functions to find the radian measures of all angles having the given trigonometric values. 10. angles whose tangent is 21.6 11. angles whose sine is 1.2 12. angles whose cosine is 0.5 13. angles whose tangent is 1.3 21.012 1 n · 2π and 2.130 1 n · 2π no solution 1.047 1 n · 2π and 5.236 1 n · 2π 0.9151 1 n · 2π and 4.057 1 n · 2π Solve each equation for u for 0 # u # 2π. 14. 2 sin u 5 !3 π3 , 2π 3 15. cos2 u 2 1 5 0 0, π 16. 2 tan u 1 3 5 tan u 1.8925, 5.034 17. cos u 1 cos u sin u 5 0 π 3π 2, 2 Lesson 14-3 In kABC, lC is a right angle. Find the remaining sides and angles. Round your answer to the nearest tenth. 18. m/A 5 298, b 5 8 /B 5 618, a 5 4.4, c 5 9.1 21. a 5 2, b 5 4 c 5 4.5, /A 5 26.68, /B 5 63.48 19. a 5 7, c 5 9 b 5 5.7, /A 5 51.18, /B 5 38.98 22. m/A 5 378, c 5 12 /B 5 538, a 5 7.2, b 5 9.6 20. m/B 5 528, b 5 10 /A 5 388, c 5 12.7, a 5 7.8 23. b 5 5, c 5 8 a 5 6.2, /B 5 38.78, /A 5 51.38 Prentice Hall Algebra 2 • Extra Practice Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 53 Name Class Date Extra Practice (continued) Chapter 14 In kRST, lS is a right angle, RS 5 24, and cos R 5 12 13 . Draw a diagram and find each value in fraction and decimal form. 24. sin R 5 , 0.385 13 25. sin T 12 , 0.923 13 26. cos T 5 , 0.385 13 27. cot R 12 , 5 2.4 28. A surveillance plane is flying at an altitude of 13 mi. The diagram shows how the visibility from the plane is defined by a circular arc limited by the tangent lines to the surface of Earth. Assume the radius of Earth to be 3950 mi. Use the diagram to find the visibility range (arc length). about 640 mi 13 mi 3950 mi not to scale 29. Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24°, and the angle of depression to the bottom of the taller building is 35°. How tall is each building? Round to the nearest foot. 140 ft, 229 ft 30. The diagram shows an experimental aircraft with sweptback triangular wings. What is the area of each wing? Round to the nearest tenth of a square foot. 246.6 ft2 14 ft 68 38 ft Prentice Hall Algebra 2 • Extra Practice Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 54 Name Class Date Extra Practice (continued) Chapter 14 Lessons 14-4 and 14-5 Use the Law of Sines or Law of Cosines. Find the measure x to the nearest tenth. 31. 43.0 C 11 13 33. 25 x 9 x A E 32. 11.3 B D 12.6 F x 10 65 32 9 F H G 13 B 34. A landscaping company received a rough sketch of a triangular property from the property owner. The sketch, shown at the right, is not to scale. The owner is asking for a price quote to sod the land. Sod costs $2 per square foot. Can the landscaper estimate the cost of the job using the information provided? If so, find the estimate. If not, explain what information is missing. Answers may vary. Sample: No; the sketch does not specify if the triangle is acute or obtuse. 234 ft 300 ft 51 A C 35. Two spotters are observing a hot-air balloon. The spotters are 1.2 mi apart and the balloon is between them. One spotter reports an angle of elevation of 68°, and the other spotter reports an angle of elevation of 84°. What is the altitude of the balloon? Round to the nearest hundredth of a mile. 2.36 mi 36. The Cairo tessellation is a tiling pattern that is used for many streets in Cairo, Egypt. The tiling uses identical pentagonal tiles. Each tile has five congruent sides but it is not a regular pentagon. You can construct the Cairo tile as shown in the figure. Start with AB. Find the midpoint M of the segment. Construct lines ME and MC at 45° to AB. Use AB as a radius to mark off points E and C. Then use the same radius to mark point D. Find the measure of /EAB to the nearest tenth of a degree. 114.3° D E C 45 A 45 M B 37. An entrepreneur wants to develop a property. The map of the property is a quadrilateral with vertices at points (5, 5), (6, 9), (11, 10), and (11, 5). Find the angle measures at each vertex to the nearest tenth of a degree. 76°, 115.3°, 78.7°, 90° Prentice Hall Algebra 2 • Extra Practice Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 55 Name Class Date Extra Practice (continued) Chapter 14 Lesson 14-6 Find each exact value. Use a sum or difference identity. 38. cos 15° !6 1 !2 4 !3 2 41. cos 390° !2 39. sin 15° !6 2 4 40. tan 315° 21 !2 42. sin 105° !6 1 4 43. tan 225° 1 Lesson 14-7 Use a double- or half-angle identity to find the exact value of each expression. 44. sin 120° Á2 45. cos 720° 1 47. cos 180° 21 48. sin 180° 0 50. sin 90° 1 51. cos 75° 3 53. sin 67.5° % 2 1 !2 46. tan 480° 2Á 3 1 49. cos 480° 22 2 2 !3 4 % 54. tan 67.5° "3 1 2 !2 2 52. tan 75° 2 1 "2 1 !3 55. cos 7.5° % 2 56. Lines /1 and /2 pass through the origin and Quadrants I and III. y Line /1 is the bisector of the angle formed by the x-axis and line /2 . Lines /2 and x 5 a intersect at (a, b). Lines /1 and x 5 a intersect at (a, c). Express c as a function of a and b. c5 "7 1 4 !3 2a2 1 a"a2 1 b2 b x=a (a, b) (a, c) a Prentice Hall Algebra 2 • Extra Practice 56 1 x O Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 2