From the top of a 150-foot tall lighthouse

Question

From the top of a 150-foot tall lighthouse, a boat is spotted with an angle of depression of 18.4º. How far is the boat from the bottom of the lighthouse? Round your answer to the nearest tenth.

Answer 1

T - top of the lighthouse

B - bottom of the lighthouse

A - the point where a boat was spotted

BA - the distance from the bottom of lighthouse to the boat: let it be "x"

TBA is a right triangle. ∠TBA is right angle.

TB is the height of lighthouse (the leg of triangle). BA is the base (another leg of triangle).

TA - hypotenuse.

TB = 150 (feet).

∠TAB = 18.4º (elevation angle). It will have the same measure as the depression angle.

cot(18.4°) = (BA)/(TB) = x/150

x = 150 • cot(18.4°) = 450.9 ≅ 451 (feet)

Answer 2

Draw and label a diagram.

Angle of elevation equals angle of depression.

d represents the distance between the boat and the lighthouse.

tan 24° 4' = 150 / d

Can you solve for d and asnwer?