Awoman 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.

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

From diagram,

In ΔOAB,

tan 18 =

tan 18 =  

∴ x =   ................ (1)

In ΔOBC

tan 14 =

tan 14 =  

y = x × tan 14 ..............(2)

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

x =

x =

∵ tan 18 + tan 14 = 0.574

∴ x = 113.2 ft

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