Question 118
Let $ABC$ be a triangle with $AB = 5$, $AC = 8$, and $\angle BAC = 60^\circ$. Let $UVWXYZ$ be a regular hexagon that is inscribed inside $ABC$ such that $U$ and $V$ lie on side $BA$, $W$ and $X$ lie on side $AC$, and $Z$ lies on side $CB$. What is the side length of hexagon $UVWXYZ$?