An observer in a lighthouse 350 feet above sea level observe

An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are beta = 8 degree and theta = 10.5 degree (see figure). How far apart are the ships? ()

Solution

Let x and y be the two ships.
Let x be the ship further away from y.
The distance from y to sea level (ground)= 350tan(8°)= 350*0.14054= 49.19 feet
The distance from x to sea level (ground)= 350tan(10.5)= 350*0.18533 = 64.86 feet
The difference between these distances is
64.86 - 49.19 = 15.67 feet