# PRACTICE PROBLEMS CH 8 and Proofs

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1 GEOM PRACTICE PROBLEMS CH 8 and Proofs Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of the missing side. The triangle is not drawn to scale. 2. a. 28 b. 100 c. 10 d. 48 a. 35 b. 49 c. 7 d Find the length of the missing side. Leave your answer in simplest radical form. a. m b. 113 m c. m d. m

2 4. a. cm b. cm c. cm d. cm 5. Wayne used the diagram to compute the distance from Ferris to Dunlap to Butte. How much shorter is the distance directly from Ferris to Butte than the distance Wayne found? a. 20 mi b. 25 mi c. 10 mi d. 35 mi 6. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain. a. yes; c. no; b. no; d. yes; 7. In triangle ABC, is a right angle and 45. Find BC. If you answer is not an integer, leave it in simplest radical form. a. 22 ft b. 22 ft c. 11 ft d. 11 ft 8. Find the length of the hypotenuse.

3 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. c. 16 d. 10. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. a. x = 7, y = 9.9 b. x = 9.9, y = 7 c. x = 4.9, y = 6.1 d. x = 6.1, y = Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

4 a. b. c. d. 12. The area of a square garden is 50 m 2. How long is the diagonal? a. 25 m b. 100 m c. m d. 10 m 13. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. a. b. c. d. 14. Not drawn to scale a. x =, y = c. x =, y = 10 b. x = 10, y = d. x = 30, y =

5 15. a. x = 17, y = c. x =, y = 17 b. x = 34, y = d. x =, y = Find the value of x and y rounded to the nearest tenth. a. x = 48.1, y = 46.4 c. x = 24.0, y = b. x = 48.1, y = d. x = 24.0, y = A piece of art is in the shape of an equilateral triangle with sides of 7 in. Find the area of the piece of art. Round your answer to the nearest tenth. a. none of these b in. 2 c in. 2 d in A sign is in the shape of a rhombus with a 60 angle and sides of 9 cm long. Find its area to the nearest tenth. a cm 2 b. 3.9 cm 2 c. 7.8 cm 2 d cm Write the tangent ratios for and. a. c. b. d.

6 Find the value of x. Round your answer to the nearest tenth. 20. a. 3.3 b. 3.1 c d a. 6.2 cm b cm c cm d cm Find the value of x to the nearest degree. 22. a. 30 b. 60 c. 70 d a. 67 b. 23 c. 83 d The students in Mr. Collin s class used a surveyor s measuring device

7 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. a ft b. 72 ft c. 308 ft d. 33 ft 25. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-foot-long shadow. Find the measure of to the nearest degree. a. 68 b. 45 c. 35 d Find the value of w, then x. Round lengths of segments to the nearest tenth. a. w = 13.3, x = 10.2 c. w = 13.3, x = 23.6 b. w = 10.8, x = 6.1 d. w = 10.8, x = Find the missing value to the nearest tenth. a b c d. 67.4

8 28. Write the ratios for sin X and cos X. a. c. b. d. 29. Find the value of x. Round to the nearest tenth. 30. a b. 10 c. 13 d. 9.7 a b c. 6.2 d. 6.5 Find the value of x. Round to the nearest degree.

9 31. a. 60 b. 27 c. 26 d a. 41 b. 36 c. 46 d Viola drives 170 meters up a hill that makes an angle of 6 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered? a m b m c m d m 34. Find the value of x. Round the length to the nearest tenth. 35. a. 7.1 cm b cm c. 9.2 cm d. 8.4 cm

10 a. 7.6 ft b ft c ft d. 7.9 ft 36. a m b m c m d m 37. 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 38. 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 40. A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 8 miles. a. Draw and label a diagram to represent this situation. b. To the nearest hundredth of a mile, how high does the highway rise in this 8-mile section? Show the steps you use to find the distance. Essay

11 41. From the top of a 210-foot lighthouse located at sea level, a boat is spotted at an angle of depression of 23. a. Draw a sketch to represent this situation. b. Use the angle of depression to find the distance from the base of the lighthouse to the boat. Explain your steps in finding the distance. c. Use another angle to verify the distance you found in part (b). Explain your steps in finding the distance and tell why your method works. d. Use the Pythagorean Theorem to find the shortest distance from the top of the lighthouse to the boat. Explain your steps in finding this distance.

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