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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.

A

$12\text{ miles}$

B

$13\text{ miles}$

C

$15\text{ miles}$

D

$16\text{ miles}$

E

$21\text{ miles}$