document.write( "Question 892409: how would I find the measurement of the sides of a triangle if I had the measurements of the angles and the measurement of the perimeter. the perimiter is a set number (240) \n" ); document.write( "

Algebra.Com's Answer #540559 by Fombitz(32388) $\"\"$ $\"About$

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You can use the law of sines.
\n" ); document.write( "Let the three angles be $\"A\"$ , $\"B\"$ and $\"C\"$ .
\n" ); document.write( "Let the three corresponding sides be $\"a\"$ , $\"b\"$ , and $\"c\"$ .
\n" ); document.write( "You know,
\n" ); document.write( " $\"a%2Bb%2Bc=240\"$
\n" ); document.write( "From the law of sines you know,
\n" ); document.write( " $\"sin%28A%29%2Fa=sin%28B%29%2Fb=sin%28C%29%2Fc\"$
\n" ); document.write( "So then from this,
\n" ); document.write( " $\"b%2Asin%28A%29=a%2Asin%28B%29\"$
\n" ); document.write( " $\"b=a%28sin%28B%29%2Fsin%28A%29%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"c%2Asin%28A%29=a%2Asin%28C%29\"$
\n" ); document.write( " $\"c=a%28sin%28C%29%2Fsin%28A%29%29\"$
\n" ); document.write( "Substituting,
\n" ); document.write( " $\"a%2Ba%28sin%28B%29%2Fsin%28A%29%29%2Ba%28sin%28C%29%2Fsin%28A%29%29=240\"$
\n" ); document.write( " $\"a%281%2Bsin%28B%29%2Fsin%28A%29%2Bsin%28C%29%2Fsin%28A%29%29=240\"$
\n" ); document.write( "Then you find $\"a\"$ and work backwards to find $\"b\"$ and $\"c\"$ .
\n" ); document.write( " \n" ); document.write( "

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