Name Class Date Extra Practice
Chapter 10
Lesson 10-1
Determine whether the given lengths can be side lengths of a right triangle.
1. 15, 36, 39
yes; 152 1 362 5 392
2. 3, 7, 10
no; 32 1 72 2 102
3. 8, 15, 17
yes; 82 1 152 5 172
4. !3, !4, !5
no; 3 1 4 2 5
5. 6, 7, 8
no; 62 1 72 2 82
6. 12, 16, 20
yes; 122 1 162 5 202
7. a 5 6, b 5 8 10
8. a 5 5, b 5 9 10.3
10. a 5 9, b 5 1 9.1
11. a 5 7, b 5 3.5 7.8
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.
9. a 5 4, b 5 10
10.8
12. a 5 1.4, b 5 2.3 2.7
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? about 19.4 ft
14. A soccer field is 80 yd long and 35 yd wide. What is the diagonal distance
across the field?
about 87.3 yd
Lesson 10-2
Simplify each radical expression
15.
18.
21.
!27
!81
!72
!50
44x4
Ä 11
"3
3
6
5
2x2
25
16. % 4 5
2
19. !25 ? !4 10
22.
"3c2
!27
c
3
50
17. % 9
5"2
3
20. !27 ? !3 9
23. !45 ? !18
9"10
Use the formula d 5 !1.5h to 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.
about 23 mi
25. Find the distance you can see to the horizon from an airplane that is 36,000 ft
above the ground.
about 232 mi
26. Find the distance you can see to the horizon from 15 ft above the ground.
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about 5 mi
Name Class Date Extra Practice (continued)
Chapter 10
Lesson 10-3
Simplify each radical expression.
27. !75 2 4!75 215"3
30. 3!300 1 2!27 36"3
33.
36.
"z 3
!5z
z"5
5
1
!2 1 1
28. !5A !20 2 !80 B 210
29. !6 A !6 2 3B 6 2 3"6
34. A !5 1 1B A !5 2 1B 4
35. A !3 1 !2 B 2 5 1 2"6
31. 5 !2 ? 3 !50 150
37.
"2 2 1
2
!2 2 2
32. !8 2 4 !2
38.
22"2
!3 1 1
!2 1 1
"6 1 "2 2 "3 2 1
2A "2 1 2B
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 A1 1 !5B : 1. The length is
25 in. What is the width?
25A "5 2 1B
;
4
7.7 in.
40. The ratio of the length of a painting to its width is A1 1 !3B : 1. The length is
40 cm. What is the width? 220A1 2 "3 B ; 14.6 cm
Lesson 10-4
Solve each radical equation. Check your solution.
41. !3x 1 4 5 1 21
42. 6 5 !8x 2 4 5
47. !3x 2 2 5 x
48. !x 1 7 5 x 1 1
44. !2x 1 5 5 !3x 1 1
4
1, 2
45. 2x 5 !6x 1 4
2
1
2,
43. 2x 5 !14x 2 6
2
3
46. !5x 1 11 5 !7x 2 1
6
x19
49. !x 1 3 5 5
1, 6
Write and solve a radical equation for each situation.
2
50. What is the diameter of a circular livestock pen if the area is 450 m 2 ? 450 5 p Q D
2 R ; 23.9 m
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 v 5 8 !h 2 2r
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? about 60 ft
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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. y 5 !x 1 5 x $ 25;
53. y 5 !x 2 2 x $ 0;
y
1
-4
-2
y
O
x
O
54. y 5 !x 1 1
4
6
y
2
x
1 2
55. y 5 !x 2 4 x $ 0
y
O
2
4
6
O
x
56. y 5 !x 2 3 x $ 3;
y
8
2
4
x $ 0;
y
6
x
O
x
1 2 3 4 5 6
57. y 5 !x 1 6
2
-2
x $ 21;
6
4
2
x
O
58. Suppose a motorcycle company uses the function
a. Graph the function.
4
6
200
Sales Volume
n 5 30 !4t 1 90 to model the sales volume n, as a
function of time t, the number of months after the
start of the advertising campaign.
2
b. Use the graph to estimate when
200 motorcycles will be sold. about 3.5 months
150
100
50
0
1
2
3
Time (months)
4
Lesson 10-6
Use kABC to find the value of the expression.
9
41
60. cos A
40
41
9
61. tan A 40
62. sin B
40
41
9
63. cos B 41
64. tan B
40
9
59. sin A
41
B
40
C
A
Find the value of each expression. Round to the nearest ten-thousandth.
65. sin 728 0.9511
66. cos 298 0.8746
67. tan 488 1.1106
68. tan 528 1.2799
69. sin 658
0.9063
70. cos 438 0.7314
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9
Name Class Date Extra Practice (continued)
Chapter 10
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 768, find the height of the tree.
Round your answer to the nearest meter. 201 m
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 28. How far is the airplane from the start
of the runway (in ground distance)? 715,906 ft (about 136 mi)
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 758 angle with the ground? about 19 ft
74. The length of a rectangular field is 100 yd and the diagonal across the field
forms an angle of 258 with the sideline. What is the length of the diagonal line?
about 110 ft
75. A pilot is flying a plane 6500 ft above the ground. The pilot begins a 38descent
to an airport runway. Find the horizontal distance between the airplane and
the start of the runway. 124,027 ft (about 23 mi)
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 68. How far away is the tower?
11,417 ft (about 2.2 mi)
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