44. Hobbies Suppose you are flying a kite. The kite string is 60 m long, and the angle of elevation of the string is 65 ° 65 degrees  from your hand. Your hand is 1 m above the ground. How high above the ground is the kite?

C Challenge

45. At a certain point in a large, level park, the angle of elevation to the top of an office building is 30 ° . 30 degrees .  If you move 400 ft closer to the building, the angle of elevation is 45 ° . 45 degrees .  To the nearest 10 ft, how tall is the building?
46. A line passes through the origin of a coordinate plane and forms a 14 ° 14 degrees  angle with the positive x-axis. What is the slope of the line? Round to the nearest hundredth.
47. Reasoning Use the definitions of sine, cosine, and tangent to simplify each expression.
    1. cos   A   ·   tan   A cosine eh middle dot tangent eh
    2. sin   A   ÷   tan A sine eh divides tangent eh
    3. sin   A   ÷   cos A sine eh divides cosine eh

Standardized Test Prep

SAT/ACT

48. What is the value of b in the proportion 3 7 = 2 b 4 b + 2 ? 3 sevenths , equals . fraction 2 b , over 4 b plus 2 end fraction . question mark
    1. 3
    2. 6
    3. 12
    4. 28
49. The profits of a large corporation can be graphed as a line that passes through ( − 3 ,   6 ) open negative 3 comma 6 close  and ( 4 ,   − 1 ) . open 4 comma minus 1 close .  Which equation represents the line?
    6. y   =   3   − x y equals 3 minus x
    7. y   =   3 x   + 1 y equals 3 x plus 1
    8. y   =   − 3 x   +   1 y equals minus 3 x plus 1
    9. y   =   x   +   3 y equals x plus 3
50. Which expression is equivalent to 3 3 12 + 2 3 ? 3 square root of 12 plus 2 square root of 3 question mark
    1. 5 3 5 square root of 3
    2. 8 3 8 square root of 3
    3. 5 15 5 square root of 15
    4. 8 12 8 square root of 12

51. Short Response Graph the solutions of the inequality − 2 x ≥ 1 negative 2 x greater than or equal to 1  on a number line.

Mixed Review

See Lesson 10-5.

Graph each function.

52. y = x + 8 y equals square root of x plus 8
53. y = x − 6 y equals , square root of x minus 6 end root
54. y = 4 x y equals 4 square root of x

See Lesson 10-1.

Determine whether the given lengths can be side lengths of a right triangle.

55. 15, 36, 39
56. 7 9 , 24 9 , 25 9 7 ninths , comma , 24 over 9 , comma , 25 over 9
57. 12, 35, 36

Get Ready! To prepare for Lesson 11-1, do Exercises 58–61.

See Lesson 8-5.

Factor each expression.

58. x 2   + x   −   12 x squared , plus x minus 12
59. x 2   +   6 x   +   8 x squared , plus 6 x plus 8
60. x 2   −   2 x   −   15 x squared , minus 2 x minus 15
61. x 2   +   9 x   +   18 x squared , plus 9 x plus 18

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