A woman standing on a hill sees a flagpole that she knows is 35 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.)

The top triangle has a vertical leg of "x", an angle opposed of 18 degrees, and a horizontal leg of d.

So tan (18) = x/d

and d = x/tan (18)

The bottom triangle has a vertical leg of "35-x", an angle opposite of 14 deg. and a horizontal leg of "d".

So tan (14) = (35-x) / d and d = (35-x) / tan (14)

Solving for "d":

x / tan (18) = (35-x) / tan14

(tan14) x = 35tan18 - (tan18) x

x (tan14 + tan18) = 35tan18

x = 11.3722/0.5742

x = 19.81 ft. (distance the lady is from the pole)