document.write( "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.) \n" ); document.write( "
Algebra.Com's Answer #412228 by lwsshak3(11628)\"\" \"About 
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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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\n" ); document.write( "draw the following diagram:
\n" ); document.write( "from the top of the hill draw a line 18º above horizontal to the top of the 60 ft pole
\n" ); document.write( "from the top of the hill draw a line 14º below horizontal to the bottom of the 60 ft pole
\n" ); document.write( "you now have 2 right triangles sharing a common horizontal line=x to the pole
\n" ); document.write( "let d=part of pole above horizontal line
\n" ); document.write( "60-d=part of pole below horizontal line
\n" ); document.write( "2 equations:
\n" ); document.write( "d/x=tan 18º
\n" ); document.write( "60-d/x=tan 14º
\n" ); document.write( "..
\n" ); document.write( "x=d/tan 18º
\n" ); document.write( "x=(60-d)/tan 14º
\n" ); document.write( "..
\n" ); document.write( "d/tan 18º=(60-d)/tan 14º
\n" ); document.write( "tan 14ºd=tan 18º(60-d)
\n" ); document.write( "tan 14ºd=tan 18º*60-tan 18ºd
\n" ); document.write( "tan 14ºd+tan 18ºd=tan 18º*60
\n" ); document.write( "d(tan 14º+tan 18º)=tan 18º*60
\n" ); document.write( "d=tan 18º*60/(tan 14º+tan 18º)
\n" ); document.write( "x=d/tan 18º=60/(tan 14º+tan 18º)=104.5 ft
\n" ); document.write( "her distance x from the pole=104.5 ft
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