Question

A woman standing on a hill sees a flagpole that she knows is 65 ft tall. The angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. Find her distance x from the pole.

Answer 1

Answer:

Let the distance between woman and pole be "x".

From diagram,

In ΔOAB,

tan 18 = $\frac{Perpendicular}{Base}$

tan 18 =  $\frac{65 -y}{x}$

∴ x =  $\frac{65 -y}{tan 18}$ ................ (1)

In ΔOBC

tan 14 = $\frac{Perpendicular}{Base}$

tan 14 =  $\frac{y}{x}$

y = x × tan 14 ..............(2)

equating (2) in (1), we get;

x = $\frac{65}{tan 18 + tan 14}$

x = $\frac{65}{0.574}$

∵ tan 18 + tan 14 = 0.574

∴ x = 113.2 ft

i.e. The her distance from the pole is 113.2 ft.