Draw a diagram: from the top of the hill draw a line 18° above the horizontal to the top of the 30 ft pole. From the top of the hill we draw a line 14° below horizontal to the bottom of the 30 ft pole. We now have 2 right triangles sharing a common horizontal line,x, to the pole. Let y=part of pole above horizontal line 30-y=part of pole below horizontal line.
We shall have the following equations: y/x=tan 18 30-y/x=tan14
x=y/tan 18 x=(30-y)/tan 14
y/tan 18=(30-y)/tan 14 y tan 14=tan 18(30-y) ytan 14=30tan 18-ytan18 y tan 14+y tan 18=30tan 18 y(tan 14+tan 18)=30*tan 18 y=(30*tan 18)/(tan 14+tan 18) x=y/tan 18=30/(tan 14+tan10)=52.2423 ft thus her distance x from the pole=52.2 ft