Precalculus
posted by Mojo on .
A woman standing on a hill sees a flagpole that she knows to be 60 ft tall. the angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees. find her horizontal distance to the flagpole.

Let H=horizontal distance to the pole
Vertical distance
=Htan(θ)
where θ is the angle of depression.
Thus
60' = Htan(θ2)Htan(θ1)
=H(tan(18°)tan(14°))
Solve for H to get
H = 60'/(tan(18°)tan(14°))
=?