51. The tallest obelisk in Europe is the Wellington Testimonial in Dublin, Ireland. The distance between an angle of 37 ° 37 degrees from the ground and the top of the obelisk and an angle of 30 ° 30 degrees from the ground to the top of the obelisk is 25 m. Use these measurements to find the height of the obelisk. Use the diagram below to set up some trigonometric equations.

    

Standardized Test Prep

SAT/ACT

52. The figure below is a rectangle. What is the value of x?

    
    Image Long Description

    1. 31.0
    2. 36.9
    3. 53.1
    4. 59.0
53. In Δ XYZ , ∠ Z cap delta is a right angle and tan X = 8 15 . tangent x equals , 8 fifteenths . . What is sin Y?
    6. 8 17 8 seventeenths
    7. 15 17 15 over 17
    8. 17 15 17 over 15
    9. 15 8 15 over 8

54. In the right triangle below, cos cos y ° = 5 13 . cosine cosine y degrees equals , 5 thirteenths . . If x + 2 z = 7.1 ( z x plus 2 z equals 7.1 open z not pictured), what is the value of z?

    

    1. 67.3
    2. 22.6
    3. − 7.76 negative , 7.76
    4. − 30.1 negative , 30.1
55. The sides of a rectangle are 25 cm and 8 cm. What is the measure of the angle formed by the short side and a diagonal of the rectangle?
    6. 17 . 7 ° 17 . 7 degrees
    7. 18 . 7 ° 18 . 7 degrees
    8. 71 . 3 ° 71 . 3 degrees
    9. 72 . 3 ° 72 . 3 degrees

Short Response

56. Find the measures of the acute angles of a right triangle, to the nearest tenth, if the legs are 135 cm and 95 cm.

Mixed Review

Find the complete solution of each equation. Express your answer in degrees. See Lesson 14-2.

57. sec 2 θ + sec θ = 0 secant squared , theta plus secant theta equals 0
58. cot θ = cot 2 θ co-tangent theta equals , co-tangent squared , theta
59. sin 2 θ + 5 sin θ = 0 sine squared , theta plus 5 sine theta equals 0

Graph each function on the interval from 0 to 2π. See Lesson 13-7.

60. y = sin ( x − π ) + 4 y equals sine open x minus pi close plus 4
61. y = 3 sin 2 ( x + π 2 ) − 5 y equals 3 sine 2 . open . x plus , pi over 2 . close . minus 5
62. y = − 2 cos ( x − π 3 ) − 4 y equals negative 2 cosine . open . x minus , pi over 3 . close . minus 4

Get Ready! To prepare for Lesson 14-4, do Exercises 63–65.

Find the area of a triangle with the given base b and height h. See p. 968.

63. b = 3 b equals 3 cm, h = 4 h equals 4 cm
64. b = 6 b equals 6 in., h = 15 h equals 15 in.
65. b = 5.2 b equals 5.2 mm, h = 12.6 h equals , 12.6 mm

Table of Contents