An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. to the nearest foot, how far is the boat from the base of the lighthouse?

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression =

      [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

Here, BC = 50 foot and

then;

or

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'