document.write( "Question 701683: I have a 30-60-90 triangle, and the long leg is 33 degrees. How do I find the short leg and hypotenuse? \n" ); document.write( "

Algebra.Com's Answer #432544 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "A $\"30-60-90\"$ triangle is a right triangle whose internal angles are $\"30\"$ , $\"+60\"$ and $\"90+degrees\"$ . \r
\n" ); document.write( "\n" ); document.write( "The three sides of a $\"30-60-90\"$ triangle have the following characteristics:\r
\n" ); document.write( "\n" ); document.write( "All three sides have $\"different\"$ lengths.
\n" ); document.write( "The shorter leg, $\"+b\"$ , is half the length of the hypotenuse, $\"c\"$ . That is,
\n" ); document.write( " $\"b=c%2F2\"$
\n" ); document.write( "The longer leg's length, $\"a\"$ , is the shorter leg times $\"sqrt%283%29\"$ . That is,
\n" ); document.write( " $\"a=b+%2Asqrt%283%29\"$ \r
\n" ); document.write( "\n" ); document.write( "so, you are given $\"c=33\"$ \r
\n" ); document.write( "\n" ); document.write( "then, you have the shorter leg $\"+b=c%2F2\"$ ...=>... $\"+b=33%2F2\"$ ...=>... $\"+b=16.5\"$ \r
\n" ); document.write( "\n" ); document.write( "and the longer leg's length is $\"a=b%2Asqrt%283%29\"$ ..=>... $\"+a=16.5%2A1.7321\"$ ...=>... $\"+a=28.545\"$ \r
\n" ); document.write( "\n" ); document.write( "check result using Pythagorean theorem:\r
\n" ); document.write( "\n" ); document.write( " $\"c%5E2=a%5E2%2Bb%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"33%5E2=28.58%5E2%2B16.5%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1089=816.8164%2B272.25\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"1089=1089.0664\"$ ...round decimal to whole number\r
\n" ); document.write( "\n" ); document.write( " $\"1089=1089\"$
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