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Published byHubert Brendan Simon Modified over 8 years ago
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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.
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Law of Sines
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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
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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.
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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.
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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.
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