Math 41 Section 9.3

Math 41 Section 9.3 - 2 + c 2 a 2 Cos A = b 2 + c 2 a 2 /...

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9.3 The Law of Cosines - the law of cosines can be used to solve SSS situations and SAS situations. Law of Cosines c 2 = a 2 + b 2 – 2ab cosC b 2 = a 2 + c 2 – 2ac cosB a 2 = b 2 + c 2 – 2bc cosA Example 1: Using the Law of Cosines to Solve an SAS Triangle Solve the triangle: a = 2, b = 3, C = 60 o Solution: c 2 = a 2 + b 2 – 2ab cosC = 4 + 9 – 2 * 2 *3 * cos 60 = 13 – (12 * ½) = 7 C = sqrt(7) For angle A: a 2 = b 2 + c 2 – 2bc cosA 2bc cosA = b
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Unformatted text preview: 2 + c 2 a 2 Cos A = b 2 + c 2 a 2 / (2bc) = 9 + 7 4 / (2 * 3sqrt(7)) = 12/(6sqrt(7)) = 2sqrt(7)/7 A = cos-1 2sqrt(7)/7 = 40.9 o For angle B: b 2 = a 2 + c 2 2ac cosB Cos B = a 2 + c 2 b 2 / (2ac) = 4 + 7 9 / (4sqrt(7)) = 1/2sqrt(7) = sqrt(7)/14 C = cos-1 sqrt(7)/14 = 79.1 o Notice that A + B + C = 40.9 + 79.1 + 60 = 180, as required....
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