1. 8-6 Law of Sines
The Law of Sines can be used to find missing parts of triangles that are not right triangles.
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 A B C a b c

2. Video Link
Law of Sines

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

4. Example 2
Solving a Triangle: Finding the measures of all of the angles and sides of a triangle.
Find the missing angles and sides of ∆PQR. Round angle measures to the nearest degree and side measures to the nearest tenth.
A: m∠R = 66,m∠Q = 59,p = 72
Answer: m∠P = 55, q ≈ 75.3, r ≈ 80.3
B: p = 32, r = 11, m∠P = 105
Answer: m∠R = 19, m∠Q = 56, q = 27.5

5. Video Link
Law of Sines – Missing Side

6. Example 3
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?
Draw a picture – label the parts – use law of sines to find the missing pieces.
Answer: about 21.1 mi, about 28.3 mi

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

8. Homework #54
p odd, 34, 38-39