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.

Answer 1

make a diagram, draw a horizontal line to the pole, let the top part of the pole be x,
then the bottom part of the pole is 60-x
call the horizontal distance to the pole = y

tan 18° = x/y
x = ytan18

tan 14 = (60-x)/y
60-x = ytan14
x = 60 - ytan14

ytan18 = 60-ytan14
ytan18 - ytan14 = 60
y(tan18 - tan14) = 60

y = 60/(tan18° - tan14°)
= ...

I will let you do the buttonpushing.

Answer 2

y= 60/(tan 18 + tan 14)