# Chapter 8 - 8.2 - Law of Cosines - 8.2 Exercises - Page 573: 34

A = $57.79^{o}$ B = $89.63^{o}$ C = $32.58^{o}$

#### 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: $cosA = \frac{13^{2} + 7^{2} - 11^{2}}{2(13)(7)}$ A = $57.79^{o}$ Finding B: $cosB = \frac{11^{2} + 7^{2} - 13^{2}}{2(11)(7)}$ B = $89.63^{o}$ Finding C: $cosC = \frac{11^{2} + 13^{2} - 7^{2}}{2(11)(13)}$ C = $32.58^{o}$ In Total: A = $57.79^{o}$ B = $89.63^{o}$ C = $32.58^{o}$

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