SOLUTION: A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pol

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Question 661252: A woman standing on a hill sees a flagpole that she knows is 60 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 by lwsshak3(11628) About Me  (Show Source):
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A woman standing on a hill sees a flagpole that she knows is 60 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.)
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draw the following diagram:
from the top of the hill draw a line 18º above horizontal to the top of the 60 ft pole
from the top of the hill draw a line 14º below horizontal to the bottom of the 60 ft pole
you now have 2 right triangles sharing a common horizontal line=x to the pole
let d=part of pole above horizontal line
60-d=part of pole below horizontal line
2 equations:
d/x=tan 18º
60-d/x=tan 14º
..
x=d/tan 18º
x=(60-d)/tan 14º
..
d/tan 18º=(60-d)/tan 14º
tan 14ºd=tan 18º(60-d)
tan 14ºd=tan 18º*60-tan 18ºd
tan 14ºd+tan 18ºd=tan 18º*60
d(tan 14º+tan 18º)=tan 18º*60
d=tan 18º*60/(tan 14º+tan 18º)
x=d/tan 18º=60/(tan 14º+tan 18º)=104.5 ft
her distance x from the pole=104.5 ft