Find the remaining sides and angles in each triangle. Round your answers to the nearest tenth.

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32. 1. Open-Ended Sketch a triangle. Specify three of its measures so that you can use the Law of Cosines to find the remaining measures.
    2. Solve for the remaining measures of the triangle.
33. Writing Given the measures of three angles of a triangle, explain how to find the ratio of the lengths of two sides of the triangle.
34. Geometry The lengths of the sides of a triangle are 7.6 cm, 8.2 cm, and 5.2 cm. Find the measure of the largest angle.
35. Navigation A pilot is flying from city A to city B, which is 85 mi due north. After flying 20 mi, the pilot must change course and fly 10 ° 10 degrees east of north to avoid a cloudbank.
    1. If the pilot remains on this course for 20 mi, how far will the plane be from city B?
    2. How many degrees will the pilot have to turn to the left to fly directly to city B? How many degrees from due north is this course?

In Δ ABC , m ∠ A = cap delta 53° and c = c equals 7 cm. Find each value to the nearest tenth.

36. Find m ∠ B m angle b for b = 6.2 b equals 6.2 cm.
37. Find a for b = 13.7 b equals , 13.7 cm.
38. Find a for b = 11 b equals 11 cm.
39. Find m ∠ C m angle c for b = 15.2 b equals , 15.2 cm.
40. Find m ∠ B m angle b for b = 37 b equals 37 cm.
41. Find a for b = 16 b equals 16 cm.

In Δ RST , t = 7  ft  cap delta and s = 13  ft. s equals 13 , ft. Find each value to the nearest tenth.

42. Find m ∠ T m angle t for r = 11 r equals 11 ft.
43. Find m ∠ T m angle t for r = 6.97 r equals , 6.97 ft.
44. Find m ∠ S m angle s for r = 14 r equals 14 ft.
45. Find r for m ∠ R = 35 ° . m angle r equals , 35 degrees .
46. Find m ∠ S m angle s for m ∠ R = 87 ° . m angle r equals , 87 degrees .
47. Find m ∠ R m angle r for m ∠ S = 70 ° . m angle s equals , 70 degrees .
48. Geometry The lengths of the adjacent sides of a parallelogram are 54 cm and 78 cm. The larger angle measures 110 ° . 110 degrees . What is the length of the longer diagonal? Round your answer to the nearest centimeter.
49. Geometry The lengths of the adjacent sides of a parallelogram are 21 cm and 14 cm. The smaller angle measures 58 ° . 58 degrees . What is the length of the shorter diagonal? Round your answer to the nearest centimeter.
50. Reasoning Does the Law of Cosines apply to a right triangle? That is, does c 2 = a 2 + b 2 − 2 a b cos C c squared , equals , eh squared , plus , b squared , minus 2 eh b cosine c remain true when ∠ C angle c is a right angle? Justify your answer.

C Challenge

51. Physics A pendulum 36 in. long swings 30 ° 30 degrees from the vertical. How high above the lowest position is the pendulum at the end of its swing? Round your answer to the nearest tenth of an inch.

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