Find his distance from the pole.

Question

A man is standing on the top of a hill and sees a flagpole he knows is 45 feet high. The angle of depression to the bottom of the pole is 12 degrees, and the angle of elevation to the top of the pole is 16 degrees. Find his distance from the pole.

Answer 1

Draw and label a diagram!

M is the location of the man

F is the point on the pole opposite the man

T is the top of the ;pole +

B is the bottom of the pole

tan 16° = TF / MF → MF tan 16° = TF

tan 12° = B F / MF → ME tan 12° = BF

MF tan 16° + MF tan 12° = TF + FB

MF tan 16° + MF tan 12° = 45

Can you solve for MF and answer?

Answer 2