Difficult# Trigonometry: Triangulating a Shipwreck

SATMAT-UI55RM

Two Coast Guard monitoring stations are placed along the coastline, $15\ miles$ apart. A sinking ship is spotted between the two stations. From one station, the line of sight to the ship makes a $63^{\circ}$ angle with the shoreline, and from the other station, the angle is $53^{\circ}$.

What is the perpendicular distance between the shipwreck and the shore? Round to the nearest whole mile.