document.write( "Question 392725: I am not positive that this is a Trigonometry problem, but I have looked through all of the other subjects and I do not know which one it would fit under, I was thinking maybe something with geometry but I am not sure. If you cannot help me with this problem, I understand. If you know what category it fits under and could let me know, that would be great! This is the problem I am stuck on: A trapezoid with bases 12 and 20 is inscribed in a semi-circle. Find the length of each leg.
\n" ); document.write( "I have looked at it for a while and just cannot seem to get anywhere. I know you will probably have to draw a diagonal to find the answers but you do not know any angle measurements or anything else about the semi-circle or trapezoid so I do not even know where to begin. Any help would be greatly appreciated and I thank you so much! If it helps at all, I am in a 10th grade honors class. Thanks again(: \n" ); document.write( "

Algebra.Com's Answer #278835 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Oh, yes, there is enough information.\r\n" );
document.write( "\r\n" );
document.write( "Let O be the center of the semicircle.  BC, which is 20 units long\r\n" );
document.write( "is a diameter of the semicircle, so OB is a radius and is 10 unit\r\n" );
document.write( "long.  \r\n" );
document.write( "\r\n" );
document.write( "Draw radius OA, which is also 10 units long.\r\n" );
document.write( "\r\n" );
document.write( "Draw OE perpendicular to both bases of the trapezoid, splitting the \r\n" );
document.write( "upper 12-unit base AD of the trapezoid into two segments AE and DE, \r\n" );
document.write( "each 6 units long.\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Triangle AEO is a right triangle and we can use the\r\n" );
document.write( "Pythagorean theorem to find OE. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we label OE as 8 units long.\r\n" );
document.write( "Draw AF parallel and equal in length to OE, which\r\n" );
document.write( "is also 8 units long:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Since AE is the same length as OF, OF is also 6 units long,\r\n" );
document.write( "and since OB is 10 units long, BF is 10-6 or 4 units long:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "Now since ABF is a right triangle, we can find AB using the\r\n" );
document.write( "Pythagorean theorm:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And CD is also \r\n" );
document.write( "\r\n" );
document.write( "or about 8.94427191 units long\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );