Question

An person in a lighthouse 350 ft above sea level observes two ships directly offshore. The angle of depression to the USS Mathematica is `4^\@` and the angle of depress to the USS Tigra is `\7.5^\@`. How far from the shoreline are the ships?

Answer 1

See below.

Explanation:

It can be seen from the diagram, that the angles of elevation from the ships to the lighthouse is the same as the angles of depression. These are alternate angles.

For USS Tigra:

It can be seen from diagram, that `tan(7.5^o)=350/a`

So distance of a is:

`tan(7.5^o)=350/a=>a=350/tan(7.5^o)=color(blue)(2658.51)`ft

For USS Mathematica:

We are looking for the distance `b`.

`tan(4^o)=350/b=>b=350/tan(4^o)=color(blue)(5005.23)`ft