document.write( "Question 1033129: John (whose line of sight is 6 feet above horizontal) is trying to estimate the height of a tall oak tree. HE first measures th angle of elevation from where he is standing as 35 degrees. He walks 30 feet closer to the tree and finds that the angle of elevation has increased by 12 degrees. Find the height of the tree. (we are learning soh cah toa) \n" ); document.write( "

Algebra.Com's Answer #647713 by Boreal(15235) $\"\"$ $\"About$

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The tree is x feet above John's line of sight.
\n" ); document.write( "When John is y feet away, the angle of elevation is 35 degrees.
\n" ); document.write( "The height of the tree is the opposite side. The distance from the tree is the adjacent side.
\n" ); document.write( "tan 35=x/y
\n" ); document.write( "===========
\n" ); document.write( "When he is (y-30) feet from the tree, the angle is now 47 degrees
\n" ); document.write( "tan 47=x/(y-30)
\n" ); document.write( "x=y tan 35
\n" ); document.write( "x=(y-30)tan 47
\n" ); document.write( "Therefore,
\n" ); document.write( "y tan 35=(y-30)tan 47
\n" ); document.write( "ytan35-ytan47=-30tan 47
\n" ); document.write( "y(tan35-tan47)=-30 tan 47
\n" ); document.write( "-0.3722y=-32.17\r
\n" ); document.write( "\n" ); document.write( "y=86.4 feet tall, but we have to add the 6 feet John is tall, so the height is 92.4 feet. \n" ); document.write( "

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