document.write( "Question 1201705: A 45-45-90 triangle is joined with a 30-60-90 triangle with a hypotenuse of 24 for the 30-60-90 triangle. Find the other 3 sides. \n" ); document.write( "

Algebra.Com's Answer #836197 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "We are not told which way the 30-60-90 triangle is turned.  So there are two\r\n" );
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document.write( "A 45-45-90 triangle is half of a square cut down its diagonal.\r\n" );
document.write( "A 30-60-90 triangle is half of an equilateral triangle cut through a vertex\r\n" );
document.write( "perpendicular to the opposite side.\r\n" );
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document.write( "The properties of all 45-45-90 triangles are:\r\n" );
document.write( "1. the two legs are equal \r\n" );
document.write( "2. the hypotenuse is  times the length of a leg.\r\n" );
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document.write( "The properties of all 30-60-90 triangles are:\r\n" );
document.write( "1. the shorter leg is half of the hypotenuse. \r\n" );
document.write( "2. the longer leg is  times the shorter leg.\r\n" );
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document.write( "First solution (below):\r\n" );
document.write( "Since the hypotenuse BC of triangle BCD is 24, its shorter leg, CD, is half of\r\n" );
document.write( "24, or 12.\r\n" );
document.write( "Since the shorter leg CD is 12, the longer leg BD is .\r\n" );
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document.write( "Since leg CD of triangle ACD is 12, the other leg AD is also 12, and the\r\n" );
document.write( "hypotenuse AC is .\r\n" );
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document.write( "So  and AB = \r\n" );
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document.write( "Second solution (drawn below):\r\n" );
document.write( "Since the hypotenuse BC of triangle BCD is 24, its shorter leg, BD, is half of\r\n" );
document.write( "24, or 12.\r\n" );
document.write( "Since the shorter leg BD is 12, the longer leg  CD is .\r\n" );
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document.write( "Since leg CD of triangle ACD is , the other leg AD is also\r\n" );
document.write( ", and the hypotenuse AC is  times .\r\n" );
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document.write( "So  and AB = \r\n" );
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document.write( "Edwin

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