Question

A woman standing on a hill sees a flagpole that she knows is 40 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

let distance form the pole = x and height of the hill = y ft

now we can set up 2 equayions
tan 18 = (40-y)/x
tan 14 = y/x

from second equation y = sxtan14 so we have:-
tan 18 = ( 40 - x tan 14) / x

x tan 18 = 40 - x tan 14
x(tan 18 + tan 14) = 40

x = 40 / (tan18 + tan 14) = 69.66 feet Answer