Chapter 8 Practice Test


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1 Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In triangle ABC, is a right angle and 45. Find BC. If you answer is not an integer, leave it in simplest radical form. C 11 ft B A a. 22 ft b. 22 ft c. 11 ft d. 11 ft 2. Find the length of the hypotenuse a. 12 b. 6 c. 5 d Find the length of the leg. If your answer is not an integer, leave it in simplest radical form a. 128 b. 8 2 c. 16 d Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth.
2 7 y 45 a. = 7, y = 9.9 b. = 9.9, y = 7 c. = 4.9, y = 6.1 d. = 6.1, y = Find the value of the variable. If your answer is not an integer, leave it in simplest radical form a. b. c. d. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form a. 2 b. c. 1 2 d. 7. y a. =, y = c. =, y = 10 b. = 10, y = d. = 30, y =
3 8. y a. = 17, y = c. =, y = 17 b. = 34, y = d. =, y = Find the value of and y rounded to the nearest tenth y 30 a. = 48.1, y = 46.4 c. = 24.0, y = b. = 48.1, y = d. = 24.0, y = Write the tangent ratios for and. P R 20 Q a. c. b. d. 11. Write the tangent ratios for and. Z 7 85 X 6 Y
4 a. c. b. d. Find the value of. Round your answer to the nearest tenth a. 3.3 b. 3.1 c d cm a. 6.2 cm b cm c cm d cm Find the value of to the nearest degree a. 30 b. 60 c. 70 d a. 67 b. 23 c. 83 d. 53
5 16. The students in Mr. Collin s class used a surveyor s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. Building 100 ft a ft b. 72 ft c. 308 ft d. 33 ft 17. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249footlong shadow. Find the measure of to the nearest degree. 100 ft A 249 ft a. 68 b. 45 c. 35 d Find the missing value to the nearest tenth. tan = 45 a b c d Write the ratios for sin A and cos A. A 4 5 C 3 B a. c. b. d. 20. Write the ratios for sin X and cos X.
6 X 5 12 Z 119 Y a. c. b. d. Find the value of. Round to the nearest tenth a b. 10 c. 13 d a b. 8.5 c d a b c d. 31.8
7 a b c. 6.2 d. 6.5 Find the value of. Round to the nearest degree a. 60 b. 27 c. 26 d a. 41 b. 36 c. 46 d A slide 4.1 meters long makes an angle of 35 with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide? 4.1 m a. 7.1 m b. 3.4 m c. 5.0 m d. 2.4 m 28. Find the value of w and then. Round lengths to the nearest tenth and angle measures to the nearest degree.
8 10 w 11 a. w = 7.7, = 44 c. w = 7.7, = 54 b. w = 6.4, = 54 d. w = 6.4, = 44 Find the value of. Round the length to the nearest tenth cm a. 7.1 cm b cm c. 9.2 cm d. 8.4 cm m a m b m c. 8.6 m d m ft a. 7.6 ft b ft c ft d. 7.9 ft
9 m a m b m c m d m yd a yd b yd c. 9 yd d yd 34. An airplane over the Pacific sights an atoll at an angle of depression of 5. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter? 4629 m a. 403 m b. 405 m c m d m 35. To approach the runway, a small plane must begin a 9 descent starting from a height of 1125 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach? 1125 ft a. 1.3 mi b. 1.4 mi c. 0.2 mi d. 7,191.5 mi
10 36. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole? a. 145 ft b. 149 ft c. 135 ft d. 139 ft 37. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to the entrance door? a. 39 b. 51 c. 53 d Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree. a. 54 b. 36 c. 46 d. 44 Short Answer 39. The diagram shows the locations of John and Mark in relationship to the top of a tall building labeled A. A ground level 4 5 Mark John a. Describe as it relates to the situation. b. Describe as it relates to the situation. 40. A forest ranger spots a fire from a 21foot tower. The angle of depression from the tower to the fire is 12. a. Draw a diagram to represent this situation. b. To the nearest foot, how far is the fire from the base of the tower? Show the steps you use to find the solution.
11 Chapter 8 Practice Test Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: L3 REF: 82 Special Right Triangles OBJ: Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 1 KEY: special right triangles 2. ANS: B PTS: 1 DIF: L2 REF: 82 Special Right Triangles OBJ: Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 1 KEY: special right triangles hypotenuse 3. ANS: B PTS: 1 DIF: L2 REF: 82 Special Right Triangles OBJ: Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 2 KEY: special right triangles hypotenuse leg 4. ANS: B PTS: 1 DIF: L3 REF: 82 Special Right Triangles OBJ: Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 2 KEY: special right triangles hypotenuse leg 5. ANS: C PTS: 1 DIF: L2 REF: 82 Special Right Triangles OBJ: Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 2 KEY: special right triangles hypotenuse leg 6. ANS: D PTS: 1 DIF: L2 REF: 82 Special Right Triangles OBJ: Using Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 4 KEY: special right triangles leg hypotenuse 7. ANS: D PTS: 1 DIF: L2 REF: 82 Special Right Triangles OBJ: Using Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 4 KEY: special right triangles leg hypotenuse 8. ANS: D PTS: 1 DIF: L2 REF: 82 Special Right Triangles OBJ: Using Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 4 KEY: special right triangles leg hypotenuse 9. ANS: D PTS: 1 DIF: L3 REF: 82 Special Right Triangles OBJ: Using Triangles STA: CA GEOM 15.0 CA GEOM 20.0 TOP: 82 Eample 4 KEY: special right triangles leg hypotenuse 10. ANS: B PTS: 1 DIF: L2 REF: 83 The Tangent Ratio TOP: 83 Eample 1 KEY: tangent ratio tangent leg opposite angle leg adjacent to angle 11. ANS: C PTS: 1 DIF: L3 REF: 83 The Tangent Ratio TOP: 83 Eample 1 KEY: leg adjacent to angle leg opposite angle tangent tangent ratio 12. ANS: C PTS: 1 DIF: L2 REF: 83 The Tangent Ratio TOP: 83 Eample 2 KEY: side length using tangent tangent tangent ratio 13. ANS: A PTS: 1 DIF: L3 REF: 83 The Tangent Ratio TOP: 83 Eample 2 KEY: side length using tangent tangent tangent ratio 14. ANS: B PTS: 1 DIF: L2 REF: 83 The Tangent Ratio TOP: 83 Eample 3
12 KEY: inverse of tangent tangent tangent ratio angle measure using tangent 15. ANS: B PTS: 1 DIF: L3 REF: 83 The Tangent Ratio TOP: 83 Eample 3 KEY: inverse of tangent tangent tangent ratio angle measure using tangent 16. ANS: C PTS: 1 DIF: L2 REF: 83 The Tangent Ratio TOP: 83 Eample 2 KEY: problem solving word problem tangent side length using tangent tangent ratio 17. ANS: D PTS: 1 DIF: L3 REF: 83 The Tangent Ratio TOP: 83 Eample 3 KEY: angle measure using tangent word problem problem solving tangent inverse of tangent tangent ratio 18. ANS: A PTS: 1 DIF: L3 REF: 83 The Tangent Ratio TOP: 83 Eample 3 KEY: angle measure using tangent 19. ANS: A PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 1 KEY: sine cosine sine ratio cosine ratio 20. ANS: C PTS: 1 DIF: L3 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 1 KEY: cosine sine sine ratio cosine ratio 21. ANS: A PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 2 KEY: cosine side length using since and cosine cosine ratio 22. ANS: D PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 2 KEY: cosine side length using since and cosine cosine ratio 23. ANS: B PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 2 KEY: sine side length using since and cosine sine ratio 24. ANS: C PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 2 KEY: sine side length using since and cosine sine ratio 25. ANS: D PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 3 KEY: inverse of cosine and sine angle measure using sine and cosine sine 26. ANS: D PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 3 KEY: inverse of cosine and sine angle measure using sine and cosine cosine 27. ANS: D PTS: 1 DIF: L2 REF: 84 Sine and Cosine Ratios TOP: 84 Eample 2 KEY: side length using since and cosine word problem problem solving sine sine ratio 28. ANS: A PTS: 1 DIF: L3 REF: 84 Sine and Cosine Ratios
13 KEY: side length using since and cosine angle measure using sine and cosine problem solving sine inverse of cosine and sine sine ratio 29. ANS: C PTS: 1 DIF: L2 TOP: 85 Eample 2 KEY: tangent side length using tangent tangent ratio 30. ANS: C PTS: 1 DIF: L2 TOP: 85 Eample 2 KEY: sine side length using since and cosine sine ratio 31. ANS: D PTS: 1 DIF: L2 TOP: 85 Eample 2 KEY: cosine side length using since and cosine cosine ratio 32. ANS: B PTS: 1 DIF: L2 TOP: 85 Eample 3 KEY: sine side length using since and cosine sine ratio angles of elevation and depression 33. ANS: B PTS: 1 DIF: L2 TOP: 85 Eample 3 KEY: tangent side length using tangent tangent ratio angles of elevation and depression 34. ANS: B PTS: 1 DIF: L2 TOP: 85 Eample 2 KEY: side length using tangent word problem problem solving tangent angles of elevation and depression tangent ratio 35. ANS: B PTS: 1 DIF: L2 TOP: 85 Eample 3 KEY: side length using since and cosine word problem problem solving sine angles of elevation and depression sine ratio 36. ANS: D PTS: 1 DIF: L3 TOP: 85 Eample 2 KEY: side length using tangent word problem problem solving tangent angles of elevation and depression tangent ratio 37. ANS: A PTS: 1 DIF: L3 KEY: angle measure using tangent word problem angles of elevation and depression problem solving tangent inverse of tangent tangent ratio 38. ANS: B PTS: 1 DIF: L3
14 KEY: angle measure using tangent word problem angles of elevation and depression problem solving inverse of tangent tangent ratio SHORT ANSWER 39. ANS: a. is the angle of elevation from Mark to the top of the building labeled A. b. is the angle of depression from the top of the building labeled A to John. PTS: 1 DIF: L2 TOP: 85 Eample 1 KEY: angles of elevation and depression multipart question word problem 40. ANS: a. Ranger 21 ft Fire b. = Use the tangent ratio. = Solve for. 99 The fire is about 99 feet from the base of the tower. PTS: 1 DIF: L3 TOP: 85 Eample 2 KEY: side length using tangent word problem multipart question problem solving tangent angles of elevation and depression tangent ratio
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