Answer
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
