Pre-Calc Exam Notes 46

Pre-Calc Exam Notes 46 - 46 Chapter 2 General Triangles 2.2...

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Unformatted text preview: 46 Chapter 2 General Triangles 2.2 The angle between two sides of a triangle is often called the included angle . Notice in the Law of Cosines that if two sides and their included angle are known (e.g. b , c , and A ), then we have a formula for the square of the third side. We will now solve the triangle from Example 2.4. Example 2.5 b = 4 a c = 5 A = 30 B C Case 3: Two sides and the angle between them. Solve the triangle ABC given A = 30 , b = 4, and c = 5. Solution: We will use the Law of Cosines to find a , use it again to find B , then use C = 180 A B . First, we have a 2 = b 2 + c 2 2 bc cos A = 4 2 + 5 2 2(4)(5) cos 30 = 6.36 a = 2.52 . Now we use the formula for b 2 to find B : b 2 = c 2 + a 2 2 ca cos B cos B = c 2 + a 2 b 2 2 ca cos B = 5 2 + (2.52) 2 4 2 2(5)(2.52) = 0.6091 B = 52.5 Thus, C = 180 A B = 180 30 52.5 C = 97.5 ....
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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.

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