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Unformatted text preview: Solve the triangle △ ABC given a = 5, b = 3, and C = 96 ◦ . Solution: A + B + C = 180 ◦ , so A + B = 180 ◦ − C = 180 ◦ − 96 ◦ = 84 ◦ . Thus, by the Law of Tangents, a − b a + b = tan 1 2 ( A − B ) tan 1 2 ( A + B ) ⇒ 5 − 3 5 + 3 = tan 1 2 ( A − B ) tan 1 2 (84 ◦ ) ⇒ tan 1 2 ( A − B ) = 2 8 tan 42 ◦ = 0.2251 ⇒ 1 2 ( A − B ) = 12.7 ◦ ⇒ A − B = 25.4 ◦ . We now have two equations involving A and B , which we can solve by adding the equations: A − B = 25.4 ◦ A + B = 84 ◦ −−−−−−−− 2 A = 109.4 ◦ ⇒ A = 54.7 ◦ ⇒ B = 84 ◦ − 54.7 ◦ ⇒ B = 29.3 ◦ We can ±nd the remaining side c by using the Law of Sines: c = a sin C sin A = 5 sin 96 ◦ sin 54.7 ◦ ⇒ c = 6.09...
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Law Of Cosines

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