Name
Class
Date
Chapter 10
Extra Practice
Lesson 10-1
Determine whether the given lengths can be side lengths of a right triangle.
1. 15, 36, 39 / 2. 3, 7, 10 / 3. 8, 15, 174. / 5. 6, 7, 8 / 6. 12, 16, 20
For the values given, a and b are legs of a right triangle. Find the length of the hypotenuse. If necessary, round to the nearest tenth.
7. a = 6, b = 8 / 8. a = 5, b = 9 / 9. a = 4, b = 1010. a = 9, b = 1 / 11. a = 7, b = 3.5 / 12. a = 1.4, b = 2.3
Use the Pythagorean Theorem to answer each question.
13. A 20-ft ladder is placed 5 ft from the base of a building. How high on the building will the ladder reach?
14. A soccer field is 80 yd long and 35 yd wide. What is the diagonal distance across the field?
Lesson 10-2
Simplify each radical expression.
15. / 16. / 17.18. / 19. / 20.
21. / 22. / 23.
Use the formulato estimate the distance d in miles to a horizon
when h is the height of the viewer's eyes above the ground. Round your answer to the nearest mile.
24. Find the distance you can see to the horizon from the top of a building that is 355 ft high.
25. Find the distance you can see to the horizon from an airplane that is 36,000 ft above the ground.
26. Find the distance you can see to the horizon from 15 ft above the ground.
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Name
Class
Date
Chapter 10
Extra Practice (continued)
Lesson 10-3
Simplify each radical expression.
27. / 28. / 29.30. / 31. / 32.
33. / 34. / 35.
36. / 37. / 38.
Find an exact solution. Then find an approximate solution to the nearest tenth.
39. The ratio of the length of a painting to its width is. The length is 25 in. What is the width?
40. The ratio of the length of a painting to its width is. The length is 40 cm. What is the width?
Lesson 10-4
Solve each radical equation. Check your solution.
41.=1 / 42. / 43.44. / 45. / 46.
47. / 48. / 49.
Write and solve a radical equation for each situation.
50. What is the diameter of a circular livestock pen if the area is 450 m2?
51. On a roller coaster ride, your speed in a loop depends on the height h of the preceding hill and the radius of the loop in feet. The equation gives the velocity v in feet per second of a car at the top of the loop. Suppose a loop has a radius of 25 ft and you want the car to have a velocity of 25 ft/s at the top of the loop. How high should the preceding hill be?
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Name
Class
Date
Extra Practice (continued)
Chapter 10
Lesson 10-5
Find the domain of each function. Then graph the function.
52. 53. 54.
55. 56. 57.
58. Suppose a motorcycle company uses the function to model the sales volume n, as a function of time t, the number of months after the start of the advertising campaign.
a. Graph the function.
b. Use the graph to estimate when
200 motorcycles will be sold.
Lesson 10-6
Use DABC to find the value of the expression.
59. sin A / 60. cos A61. tan A / 62. sin B
63. cos B / 64. tan B
Find the value of each expression. Round to the nearest ten-thousandth.
65. sin 72° / 66. cos 29° / 67. tan 48°68. tan 52° / 69. sin 65° / 70. cos 43°
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Name
Class
Date
Chapter 10
Extra Practice (continued)
71. A forester is 50 m from the base of a tree and measures the angle between the ground and the top of the tree. If the angle is 76°, find the height of the tree. Round your answer to the nearest meter.
72. A pilot is flying at an altitude of 25,000 ft. The angle of depression from her position to the start of the runway is 2°. How far is the airplane from the start of the runway (in ground distance)?
Use trigonometric ratios to answer each question.
73. A painter leans a 20-ft ladder up against the side of a house making a right triangle. How far up the side of the house will the top of the ladder rest if the ladder makes a 75° angle with the ground?
74. The length of a rectangular field is 100 yd and the diagonal across the field forms an angle of 25° with the sideline. What is the length of the diagonal line?
75. A pilot is flying a plane 6500 ft above the ground. The pilot begins a 3° descent to an airport runway. Find the horizontal distance between the airplane and the start of the runway.
76. While hiking you see a 100-ft observation tower on top of a 1100-ft hill. The angle of elevation to the top of the tower is 6°. How far away is the tower?
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