# Chapter 8 - 8.2 - Law of Cosines - 8.2 Exercises - Page 573: 32

$c= 12.72$ A = $47.61^{o}$ B = $62.39^{o}$

#### 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 c: $c^{2} = 10^{2} + 12^{2} - 2(10)(12)cos(70^{o})$ $c= 12.72$ We can use the Alternative Form of the Law of Cosines to find A: $cosA = \frac{12^{2} + 12.72^{2} - 10^{2}}{2(12)(12.72)}$ A = $47.61^{o}$ We can use the Alternative Form of the Law of Cosines to find B: $cosB = \frac{10^{2} + 12.72^{2} - 12^{2}}{2(10)(12.72)}$ B = $62.39^{o}$ In Total: $c= 12.72$ A = $47.61^{o}$ B = $62.39^{o}$

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