## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 8 - 8.2 - Law of Cosines - 8.2 Exercises - Page 573: 15

#### Answer

A = $132.77^{o}$ B = $31.91^{o}$ C = $15.32^{o}$

#### 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 Alternative Form of the Law of Cosines for each of the angles. Finding A: $cosA = \frac{1.8^{2} + 0.9^{2} - 2.5^{2}}{2(1.8)(0.9)}$ A = $132.77^{o}$ Finding B: $cosB = \frac{2.5^{2} + 0.9^{2} - 1.8^{2}}{2(2.5)(0.9)}$ B = $31.91^{o}$ Finding C: $cosC = \frac{2.5^{2} + 1.8^{2} - 0.9^{2}}{2(2.5)(1.8)}$ C = $15.32^{o}$ In Total: A = $132.77^{o}$ B = $31.91^{o}$ C = $15.32^{o}$

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