trig
posted by Dominic on .
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.)

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 65h
You now have 2 rightangled triangles
for the top one:
tan18° = h/x
h = xtan18
for the bottom part:
tan14 = (65h)/x
xtan14 = 65h
h = 65  xtan14
then xtan18 = 65  xtan14
xtan18  xtan14 = 65
x(tan18tan14) = 65
x = 65/(tan18+tan14) = 113.2