document.write( "Question 1169665: cindy is standing at a point A west of a mountain. From point A, the angle of elevation to the top of the mountain is 32 degrees. From point B, which is 8325 feet to the east of point A (and east of the mountain) the angle of elevation to the top of the mountain is 42 degrees. Determine the height of the mountain to the nearest tenth of a foot. \n" ); document.write( "
Algebra.Com's Answer #794516 by Boreal(15235)\"\" \"About 
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Draw this
\n" ); document.write( "x distance from point A to the base of the mountain directly under the summit.
\n" ); document.write( "8325-x from the base to point B
\n" ); document.write( "tan 42= h/(8325-x)
\n" ); document.write( "tan 32=h/x
\n" ); document.write( "(8325-x)*tan 42=h=x tan 32
\n" ); document.write( "tan 32/tan 42=(8325-x)/x
\n" ); document.write( "0.6940x=(8325-x)
\n" ); document.write( "1.6940x=8325 ft
\n" ); document.write( "x=4914.40 feet to the base,
\n" ); document.write( "tan 32=h/4914.40=0.6249
\n" ); document.write( "so h=3070.9 feet.\r
\n" ); document.write( "\n" ); document.write( "check for the other side
\n" ); document.write( "B is therefore 3410.6 feet from the base.
\n" ); document.write( "If the height is 3070.9 feet, then tangent is 3070.9/3410.6 and that is 42 degrees.\r
\n" ); document.write( "\n" ); document.write( "The mountaintop is 3070.9 feet above the observer.\r
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