Moderate# Plane Sighting: Angle of Elevation and Law of Sines

TRIG-5KW4XL

A plane is flying in a straight line parallel to the ground above NYC. It flies over Time Square and a short time later over the Statue of Liberty, approximately 8 miles away from Time Square. A short time after it passes over the Statue of Liberty, the angle of elevation from Time Square is $45^{ \circ}$ and the angle of elevation from the statue of liberty $75^{ \circ }$.

What is the altitude of the plane? Round to one decimal place.