Solve the Problem $15 ^ { \circ } 30 ^ { \prime }$

Multiple Choice

Solve the problem.
-A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is $15 ^ { \circ } 30 ^ { \prime }$ . When the boat stops, the angle of depression is $46 ^ { \circ } 19 ^ { \prime }$ . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round to the nearest foot.

A) $575 \mathrm { ft }$
B) $530 \mathrm { ft }$
C) $515 \mathrm { ft }$
D) $553 \mathrm { ft }$