An in-line skater skates on a fitness trail along the Pacific Ocean from point $A$ to point $B$. As shown below, two streets intersecting at point $C$ also intersect the trail at $A$ and $B$. In her car, the skater found the lengths of $A C$ and $B C$ to be approximately $0.5 \mathrm{mi}$ and $1.3 \mathrm{mi}$, respectively. From a map, she estimates the included angle at $C$ to be $110^{\circ} .$ How far did she skate from $A$ to $B ?$
CAN'T COPY THE FIGURE