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. (Round your answer to one decimal place.)

Answer 1

Draw the woman on the hill with her line of sight touching the pole somewhere in the middle.
label her line of sight x, the top part of the pole h and the bottom part of the pole 65-h
You now have 2 right-angled triangles
for the top one:
tan18° = h/x
h = xtan18

for the bottom part:
tan14 = (65-h)/x
xtan14 = 65-h
h = 65 - xtan14

then xtan18 = 65 - xtan14
xtan18 - xtan14 = 65
x(tan18-tan14) = 65
x = 65/(tan18+tan14) = 113.2

Answer 2

The - symbols in the first and second lines before the last should be +