52. 1. Find the length of the altitude to P Q ¯ p q bar in the triangle below.

       

    2. Find the area of Δ PQR cap delta .

53. Reasoning If you solve for cos A in the Law of Cosines, you get cos A = b 2 + c 2 − a 2 2 b c . cosine eh equals . fraction b squared , plus , c squared , minus , eh squared , over 2 b c end fraction . .

    1. Use this formula to explain how cos A can be positive, zero, or negative, depending on how b 2 + c 2 b squared , plus , c squared compares to a 2 . eh squared , .
    2. What does this tell you about ∠ A angle eh in each case?

Standardized Test Prep

GRIDDED RESPONSE

Use the diagram for Exercises 54–59. Angle measures are in degrees. Give each answer to the nearest tenth.

SAT/ACT

54. Let a = 23.2 eh equals , 23.2 , b = 18.5 b equals , 18.5 , and m ∠ C = m angle c equals 42. Find c.
55. Use the information in Question 54 to find m ∠ A . m angle eh .
56. Suppose a = 45.25 eh equals , 45.25 , b = 39.75 b equals , 39.75 , and c = 20.65 c equals , 20.65 . Find m ∠ B . m angle b .
57. Use the information in Question 56 to find m ∠ C . m angle c .
58. Suppose b = 11.0 b equals , 11.0 , c = 11.7 c equals , 11.7 , and m ∠ A = m angle eh equals 22. Find the length of the altitude from A.
59. Use the information in Question 58 to find the area of Δ ABC cap delta to the nearest tenth.

Mixed Review

60. In Δ RST , m ∠ R = 37 ° , m ∠ T = 59 ° , cap delta and T S = 12 t s equals 12 in. Find RS. See Lesson 14-4.
61. In Δ JKL , m ∠ L = 71 ° , j = 11 cap delta m, and m ∠ K = 46 ° . m angle k equals , 46 degrees . Find k.
62. In Δ MNP , m ∠ N = 42 ° , n = 21 cap delta in., and m ∠ M = 57 ° . m angle m equals , 57 degrees . Find m.
63. In Δ DEF , m ∠ F = 91 ° , d = 17 cap delta mm, and f = 21 f equals 21 mm. Find m ∠ D . m angle d .

Identify the period and describe two asymptotes for each function. See Lesson 13-6.

64. y = y equals tan 0. 5 θ 5 theta
65. y = tan 3 π 2 θ y equals tangent . fraction 3 pi , over 2 end fraction , theta
66. y = tan ( − 3 θ ) y equals tangent open negative 3 theta close
67. y = tan π θ y equals tangent pi theta

Get Ready! To prepare for Lesson 14-6, do Exercises 68–71.

Complete the identities. See Lesson 14-1.

68. csc θ = 1   co-secant theta equals , fraction 1 , over table with 1 row and 1 column , row1 column 1 , , end table end fraction
69. sec θ = 1   secant theta equals , fraction 1 , over table with 1 row and 1 column , row1 column 1 , , end table end fraction
70. cos 2 θ + sin 2 θ = □ cosine squared , theta plus , sine squared , theta equals white square
71. 1 + cot 2 θ = □ 1 plus , co-tangent squared , theta equals white square

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