# Chapter 7 - Quiz (Sections 7.1-7.3) - Page 326: 10

The distance between the two towns is 3921 meters

#### Work Step by Step

Let $a = 3428~m$, let $b = 5631~m$, and let angle $C = 43.33^{\circ}$. Let $c$ be the distance between the two towns. We can use the law of cosines to find $c$, the length of the line opposite the angle $C$: $c^2 = a^2+b^2-2ab~cos~C$ $c = \sqrt{a^2+b^2-2ab~cos~C}$ $c = \sqrt{(3428~m)^2+(5631~m)^2-(2)(3428~m)(5631~m)~cos~43.33^{\circ}}$ $c = \sqrt{15376718~m^2}$ $c = 3921~m$ The distance between the two towns is 3921 meters

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