document.write( "Question 964063: a shelf is built into the corner of a room whose walls meet at an angle of 120 degree. Find the area of the shelf space if its front edge is 24cm and the other two edges are equal.
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Algebra.Com's Answer #589320 by macston(5194) $\"\"$ $\"About$

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Bisecting the angle of the wall to midpoint of front edge forms two 30-60-90 triangles.
\n" ); document.write( "1/2 the front edge is 12 cm and this is the long leg of the triangle. The ratio of long leg/short leg= $\"sqrt%283%29\"$ so:
\n" ); document.write( " $\"12%2Fsqrt%283%29\"$ =6.93 cm is the short leg of the 30-60-90, which is the height of the triangle formed by the shelf, with the front edge as base.
\n" ); document.write( "Area=(1/2)(base)(height)
\n" ); document.write( "Area=1/2(24cm)(6.93cm)
\n" ); document.write( "Area=83.14 sq cm
\n" ); document.write( "ANSWER: The area of the shelf is 83.14 square centimeters. \n" ); document.write( "

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