Posted by **Dominic** on Wednesday, September 21, 2011 at 3:13am.

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.)

- trig -
**Reiny**, Wednesday, September 21, 2011 at 8:05am
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

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