document.write( "Question 1116483: find the area of the largest square that can be cut from a sector of a circle radius 8 cm and a central 120 degree \n" ); document.write( "

Algebra.Com's Answer #731623 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let the square be ABCD.\r\n" );
document.write( "\r\n" );
document.write( "Side of the square = AB = PQ = 2OQ.\r\n" );
document.write( "\r\n" );
document.write( "Since triangle OBQ is a 30°,60°,90° triangle, its longer\r\n" );
document.write( "leg is  times its shorter leg.\r\n" );
document.write( "\r\n" );
document.write( "We let its shorter leg BQ be x, then its longer leg OQ\r\n" );
document.write( "is .\r\n" );
document.write( "\r\n" );
document.write( "Since  = OQ = PQ/2 = AB/2,\r\n" );
document.write( "\r\n" );
document.write( "BC = 2∙OQ = .\r\n" );
document.write( "\r\n" );
document.write( "OC = radius = 8\r\n" );
document.write( "\r\n" );
document.write( "Using Pythagorean theorem on right triangle OQC\r\n" );
document.write( "\r\n" );
document.write( "OQ² + QC² = OC²\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Solve that and get \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So one side of the square is twice that, or 2x, which is\r\n" );
document.write( "\r\n" );
document.write( " = side of square.\r\n" );
document.write( "\r\n" );
document.write( "Therefore the area of the square is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "or \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );