Question

In the diagram below, the angle of depression from the top of the lighthouse to a speed boat is 27 degrees.  The base of the lighthouse is 33 ft away from the boat.   Determine the height of the lighthouse, to the nearest tenth of a foot.​

Answer 1

breh

Explanation:

Answer 2

=

412

feet

Explanation:

The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:

90°−27°

=63°

The distance to the boat is the side opposite the angle of

63°

while the height of the lighthouse is the adjacent side.

opposite

adjacent

=tan 63°

distance

210=tan 63°

distance=210×tan 63°=412 feet