document.write( "Question 528153: if the hypotenuse of an isosceles triangle is 11 and the angles at the hypotenuse are 45 degrees, how long are the legs? \n" ); document.write( "

Algebra.Com's Answer #349153 by KMST(5328) $\"\"$ $\"About$

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Since \"hypotenuse\" is mentioned, it would be assumed to be a right triangle from the start. Being also isosceles, it is known that it will have two 45 degree angles on the hypotenuse, but it is reassuring that the problem says so.
\n" ); document.write( "Being an isosceles right triangle, the length of both legs is the same. Let's call it $\"x\"$
\n" ); document.write( "Pythagoras' theorem says that in this case
\n" ); document.write( " $\"x%5E2%2Bx%5E2=11%5E2\"$ so
\n" ); document.write( " $\"2x%5E2=11%5E2\"$
\n" ); document.write( " $\"x%5E2=11%5E2%2F2\"$ and
\n" ); document.write( " $\"x=sqrt%2811%5E2%2F2%29=11sqrt%282%29%2F2\"$ \n" ); document.write( "

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