# Chapter 6 - Section 6.2 - The Law of Cosines - Exercise Set - Page 731: 42

The distance from point A to point B equals $113.5$ yards

#### Work Step by Step

Let us notate with $c$ the distance from point A to point B in the triangle. Then we can apply the law of cosines since we know what $a,b$ and $\gamma$ are. $a = 105$ yards, $b = 65$ yards and angle $\gamma = 80$ degrees. We just need to plug in these values into the formula and we get our answer: $c^{2} = a^{2}+b^{2}-2(ab) cos\gamma$ $c^{2} = 105^{2}+65^{2}-2(105*65)cos 80^{\circ}$ $c^{2} = 11025+4225-13650 * cos 80^{\circ}$ $c^{2} = 12879.7$ Then we just take the square root of 12879.7 and we have our answer: $c = \sqrt {12879.7}$ $c = 113.5$

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