8 6 Law of Sines n The Law

8 -6 Law of Sines n The Law of Sines can be used to find missing parts of triangles that are not right triangles. n Theorem 8. 8: Let ∆ABC be any triangle with a, b, and c representing the measures of the sides opposite the angles with measures A, B, and C, respectively. Then B c A a b C

Video Link n. Law of Sines

Let’s review the Proof for the Law of Sines on page 471. n Example 1 n A: If m∠B = 32, m∠C = 51, c = 12, find a. n Example 1 n B: If a = 22, b = 18, m∠A = 25, find m∠B.

Example 2 n Solving a Triangle: Finding the measures of all of the angles and sides of a triangle. n Find the missing angles and sides of ∆PQR. Round angle measures to the nearest degree and side measures to the nearest tenth. n A: m∠R = 66, m∠Q = 59, p = 72 n Answer: m∠P = 55, q ≈ 75. 3, r ≈ 80. 3 n B: p = 32, r = 11, m∠P = 105 n Answer: m∠R = 19, m∠Q = 56, q = 27. 5

Video Link n. Law of Sines – Missing Side

Example 3 n Two radar stations that are 35 miles apart located a plane at the same time. The first station indicated that the position of the plane made an angle of 37° with the line between the stations. The second station indicated that it made an angle of 54° with the same line. How far is each station from the plane? n Draw a picture – label the parts – use law of sines to find the missing pieces. n Answer: about 21. 1 mi, about 28. 3 mi

Key Concepts n The Law of Sines can be used to solve a triangle in the following cases. n Case 1: You know the measures of two angles and any side of a triangle. (AAS or ASA) n Case 2: You know the measures of two sides and an angle opposite one of these sides of the triangle. (SSA) n Handout – Extra Examples for additional understanding.

Homework #54 n p. 475 13 -29 odd, 34, 38 -39