The Law of Sines and Law of Cosines Chapter 8.6 The Law of Sines and Law of Cosines

Concept

Example 1 Find p. Round to the nearest tenth. Law of Sines (AAS or ASA) Find p. Round to the nearest tenth. We are given measures of two angles and a nonincluded side, so use the Law of Sines to write a proportion.

Example 1 Find c to the nearest tenth. A. 4.6 B. 29.9 C. 7.8 D. 8.5

Example 2 Find x. Round to the nearest tenth. Law of Sines (ASA) 6 57°

Example 2 Find x. Round to the nearest degree. A. 8 B. 10 C. 12 D. 14 43° x

Concept

Example 3 Find x. Round to the nearest tenth. Law of Cosines (SAS) Find x. Round to the nearest tenth. Use the Law of Cosines since the measures of two sides and the included angle are known.

Example 3 Find r if s = 15, t = 32, and mR = 40. Round to the nearest tenth. A. 25.1 B. 44.5 C. 22.7 D. 21.1

Example 4 Find mL. Round to the nearest degree. Law of Cosines Law of Cosines (SSS) Find mL. Round to the nearest degree. Law of Cosines Simplify.

Example 4 Find mP. Round to the nearest degree. A. 44° B. 51° C. 56°

Example 5 Indirect Measurement AIRCRAFT From the diagram of the plane shown, determine the approximate width of each wing. Round to the nearest tenth meter.

Example 5 The rear side window of a station wagon has the shape shown in the figure. Find the perimeter of the window if the length of DB is 31 inches. Round to the nearest tenth. A. 93.5 in. B. 103.5 in. C. 96.7 in. D. 88.8 in.

Example 6 Solve triangle PQR. Round to the nearest degree. Solve a Triangle Solve triangle PQR. Round to the nearest degree. Since the measures of three sides are given (SSS), use the Law of Cosines to find mP. p2 = r2 + q2 – 2pq cos P Law of Cosines 82 = 92 + 72 – 2(9)(7) cos P p = 8, r = 9, and q = 7

Example 6 Solve ΔRST. Round to the nearest degree. A. mR = 82, mS = 58, mT = 40 B. mR = 58, mS = 82, mT = 40 C. mR = 82, mS = 40, mT = 58 D. mR = 40, mS = 58, mT = 82

Concept