document.write( "Question 1087601: Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24°, and the angle of depression to the bottom of the taller building is 35°. How tall is each building? \n" ); document.write( "

Algebra.Com's Answer #701910 by mathmate(429) $\"\"$ $\"About$

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Question:
\n" ); document.write( "Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24°, and the angle of depression to the bottom of the taller building is 35°. How tall is each building?
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\n" ); document.write( "Solution:
\n" ); document.write( "Let the top and bottom of the taller building be points T and B respectively.
\n" ); document.write( "Let the top of the shorter building be the point S.
\n" ); document.write( "Finally, let the point on the taller building at the same elevation as the top of the shorter building be M.\r
\n" ); document.write( "\n" ); document.write( "Then TMS forms a right triangle, with base MS=200', and angle MST=24°
\n" ); document.write( "The length mMT=MStan(24°)=89.0'
\n" ); document.write( "Similarly for right triangle MSB, the length mMB=MS*tan(35°)=140.0'\r
\n" ); document.write( "\n" ); document.write( "Total height of taller building = BT=MB+BT=89.0+140.0=229'
\n" ); document.write( "Height of shorter building = BT = 140'
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