## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 8 - 8.2 - Law of Cosines - 8.2 Exercises - Page 573: 31

#### Answer

$b = 5.26$ A = $102.44^{o}$ C = $37.56^{o}$

#### Work Step by Step

Note: The Standard Form of the Law of Cosines is: $a^{2} = b^{2} + c^{2} - 2bc(cosA)$ Note: The Alternative Form of the Law of Cosines is: $cosA = \frac{b^{2} + c^{2} - a^{2}}{2bc}$ To solve the triangle, we need to find A, b, and C. We can use the Standard Form of the Law of Cosines to find b: $b^{2} = 8^{2} + 5^{2} - 2(8)(5)cos(40^{o})$ $b = 5.26$ We can use the Alternative Form of the Law of Cosines to find A: $cosA = \frac{5.26^{2} + 5^{2} - 8^{2}}{2(5.26)(5)}$ A = $102.44^{o}$ We can use the Alternative Form of the Law of Cosines to find C: $cosC = \frac{8^{2} + 5.26^{2} - 5^{2}}{2(8)(5.26)}$ C = $37.56^{o}$ In Total: $b = 5.26$ A = $102.44^{o}$ C = $37.56^{o}$

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