C Challenge

34. Sailing Buoys are located in the sea at points A, B, and C. ∠ angle ACB is a right angle. A C = 3.0 eh c equals 3.0 mi, B C = 4.0 b c equals 4.0 mi, and A B = 5.0 eh b equals 5.0 mi. A ship is located at point D on A B ¯ eh b bar so that m ∠ m angle ACD = 30 ° . equals , 30 degrees . How far is the ship from the buoy at point C? Round your answer to the nearest tenth of a mile.

    

35. Writing Suppose you know the measures of all three angles of a triangle. Can you use the Law of Sines to find the lengths of the sides? Explain.

Standardized Test Prep

SAT/ACT

36. In Δ GDL , m ∠ D = 57 ° , D L = 10.1 cap delta , and G L = 9.4 g l equals 9.4 . What is the best estimate for m ∠ G m angle g ?
    1. 64 ° 64 degrees
    2. 51 ° 51 degrees
    3. 39 ° 39 degrees
    4. 26 ° 26 degrees
37. For which set of given information can you compute the area of Δ ABC cap delta ?
    6. m ∠ C = 58 ° , c = 23 m angle c equals , 58 degrees comma , c equals 23
    7. m ∠ B = 26 ° , a = 43 m angle b equals , 26 degrees comma , eh equals 43
    8. m ∠ C = 58 ° , a = 43 , c = 23 m angle c equals , 58 degrees comma , eh equals 43 comma c equals 23
    9. m ∠ C = 26 ° , a = 43 , b = 23 m angle c equals , 26 degrees comma , eh equals 43 comma b equals 23
38. Two points in front of a tall building are 250 m apart. The angles of elevation of the top of the building from the two points are 37 ° 37 degrees and 13 ° . 13 degrees . What is the best estimate for the height of the building?
    1. 150 m
    2. 138 m
    3. 83 m
    4. 56 m

Short Response

39. Two sides of a scalene triangle are 9 m and 14 m. The area of the triangle is 31.5 m 2 . 31.5 , m squared , . Find the measure of one of the angles of the triangle to the nearest tenth of a degree. Show your work.

Mixed Review

Sketch one cycle of the graph of each sine function. See Lesson 13-4.

40. y = 4 sin θ y equals 4 sine theta
41. y = 4 sin π θ y equals 4 sine pi theta
42. y = sin 4 θ y equals sine 4 theta

Let u = ( − 2 , 3 ) , v = ( 1 , 4 ) ,  and  w = ( 4 , − 1 ) . u equals open negative 2 comma 3 close comma v equals open 1 comma 4 close comma , and , w equals open 4 comma negative 1 close . Find the component form of each vector. See Lesson 12-6.

43. u + v u plus v
44. v + w v plus w
45. u − v u minus , v
46. u − w u minus , w

Get Ready! To prepare for Lesson 14-5, do Exercises 47–50.

Find each angle measure to the nearest tenth of a degree. See Lesson 14-3.

47. cos − 1 3 5 cosine super negative 1 end super . 3 fifths
48. tan − 1 0.4569 tangent super negative 1 end super . 0.4569
49. sin − 1 5 8 sine super negative 1 end super . 5 eighths
50. tan − 1 2 tangent super negative 1 end super . square root of 2

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