document.write( "Question 827127: the hypotenuse of a right isosceles triangle is 5 cm long.
\n" ); document.write( "Write an exact expression for the base and the height of the right triangle, useing primary trigonmetric ratios?
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Algebra.Com's Answer #498516 by KMST(5347) $\"\"$ $\"About$

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The length of each leg is $\"5sqrt%282%29%2F2\"$ $\"cm\"$ .
\n" ); document.write( "That may be the expected answer.
\n" ); document.write( "You could also say that one of the legs is the base,
\n" ); document.write( "between angles measuring $\"90%5Eo\"$ and $\"45%5Eo\"$ ,
\n" ); document.write( "and the other leg is the height.
\n" ); document.write( "Then $\"base=hypotenuse%2Acos%2845%5Eo%29\"$ and $\"height=hypotenuse%2Asin%2845%5Eo%29\"$
\n" ); document.write( "We know that $\"cos%2845%5Eo%29=sqrt%282%29%2F2\"$ and $\"sin%2845%5Eo%29=sqrt%282%29%2F2\"$ .
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\n" ); document.write( "The length of the legs of the right isosceles triangle can also be calculated based on the Pythagorean theorem, without even mentioning trigonometric ratios.
\n" ); document.write( "If $\"x\"$ $\"cm\"$ = length of the legs of the right isosceles triangle,
\n" ); document.write( "according to the Pythagorean theorem,
\n" ); document.write( " $\"x%5E2%2Bx%5E2=5%5E2\"$
\n" ); document.write( " $\"2x%5E2=5%5E2\"$
\n" ); document.write( " $\"x%5E2=5%5E2%2F2\"$
\n" ); document.write( " $\"x=sqrt%285%5E2%2F2%29%5D%5D%5D%0D%0A%7B%7B%7Bx=sqrt%285%5E2%29%2Fsqrt%282%29\"$
\n" ); document.write( " $\"x=5%2Fsqrt%282%29\"$ , but since we do not like seeing square roots in denominators, we rationalize,
\n" ); document.write( " $\"x=5sqrt%282%29%2F%28sqrt%282%29%2Asqrt%282%29%29\"$
\n" ); document.write( " $\"x=5sqrt%282%29%2F2\"$ \n" ); document.write( "

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