1. Section 5.6 The Law of Sines Objective: Students will be able to: 1.Solve triangles using the Law of Sines if the measures of 2 angles and a side are given. 2.Find the area of a triangle if the measures of 2 sides and the included angle or the measures of 2 angles and a side are given.

2. Law of Sines

3. Example 1: Solve  ABC if A = 24°, B = 62°, and a = 21.4. First, find the measure of  C. C = 180° - (24° + 62°) or 94° Use the Law of Sines to find b and c. 46.45531404  b52.48573257  c

4. Example 2: The angle of depression from a window of a house to the front edge of the swimming pool is 26.6°. The angle of depression from this same window to the back edge of the swimming pool is 15.3°. The length of the pool is 25 feet. If a person looks out the window, about how far is he from the front edge of the pool? *** Make a diagram of the problem. Remember that the angle of elevation is congruent to the angle of depression because they are alternate interior angles. First, find .  = 26.6° - 15.3° or 11.3° Use the Law of Sines to find d. d  33.66652748 The person would be about 33.7 feet from the front edge of the pool.

5. Example 3: Find the area of  ABC if b = 14.8, c = 10.2, and A = 54°12. K  61.21909706 The area of  ABC is about 61.2 square units.

6. Example 4: Find the area of  DEF if e = 18.6, E = 78.2°, and F = 41.3°. First find the measure of  D. D = 180° - (78.2° + 41.3°) or 60.5° Then, find the area of the triangle. K  101.5111719 The area of  DEF is about 101.5 square units.