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Law of Cosines

Law of Cosines. By Amber Wolfe and Savannah Guenther. Introduction. Equation. Use the equation below for non-right triangles given (side-angle-side) or (side-side-side) to solve for either an angle or a side. Example 1. Solving a triangle (SAS) Given ABC , a=11, b=5, C=20

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Law of Cosines

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  1. Law of Cosines By Amber Wolfe and Savannah Guenther

  2. Introduction

  3. Equation • Use the equation below for non-right triangles given (side-angle-side) or (side-side-side) to solve for either an angle or a side.

  4. Example 1 • Solving a triangle (SAS)Given ABC, a=11, b=5, C=20 c2 =a2 + b2 – 2ab cosC = 112 + 52 -2(11)(5) cos(20) = 42.634...c = √42.634... = 6.5 A 5 20 C B 11

  5. A Example 2 7 5 Solving a triangle (SSS)Given ABC, a=9, b=7, c=5 a2 =b2 + c2 – 2bc cos A 92 + 72 -2(7)(5) cos A 70 cos A = -7 A = cos-1 (-0.1) = 95.7 b2 =a2 + c2 – 2ac cos B 72 = 92 + 52 – 2(9)(5) cos B 90 cos B = 57 B = cos-1 (57/90) = 50.7 C B 9 Then C = 180 – 95.7 – 50.7 = 33.6

  6. References • www.mathbook.com • www.dudelol.com • www.paworldmathclass.web.com • Precalculus math book • Test #4 Practice Quiz

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