document.write( "Question 934849: The area of a triangle is 40 cm squared. Find the length of the side included between the angles A=30 degrees and B=50 degrees. \n" ); document.write( "

Algebra.Com's Answer #567895 by KMST(5328) $\"\"$ $\"About$

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Let $\"a\"$ , $\"b\"$ . and $\"c\"$ be the sides' lengths, in cm.
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$\"area%5BABC%5D=%281%2F2%29%2Ac%2Ab%2Asin%28A%29\"$ --> $\"area%5BABC%5D=%281%2F2%29%2Ac%2Ab%2Asin%2830%5Eo%29\"$ --> $\"40=%281%2F2%29c%2Ab%2A%281%2F2%29\"$ --> $\"40=c%2Ab%2F4\"$
\n" ); document.write( " $\"C=180%5Eo-30%5Eo-50%5Eo\"$ ---> $\"C=100%5Eo\"$
\n" ); document.write( "Law of sines says that
\n" ); document.write( " $\"b%2Fsin%28B%29=c%2Fsin%28C%29\"$ ,
\n" ); document.write( "so $\"b%2Fsin%2850%5Eo%29=c%2Fsin%28100%5Eo%29\"$ ---> $\"b=c%2Asin%2850%5Eo%29%2Fsin%28100%5Eo%29\"$
\n" ); document.write( " $\"system%2840=c%2Ab%2F4%2Cb=c%2Asin%2850%5Eo%29%2Fsin%28100%5Eo%29%29\"$ ---> $\"40=c%2Ac%2Asin%2850%5Eo%29%2F4sin%28100%5Eo%29\"$ ---> $\"40=c%5E2%2Asin%2850%5Eo%29%2F4sin%28100%5Eo%29\"$ ---> $\"c%5E2=4%2A40sin%28100%5Eo%29%2Fsin%2850%5Eo%29\"$ ---> $\"c%5E2=160sin%28100%5Eo%29%2Fsin%2850%5Eo%29\"$
\n" ); document.write( "So, $\"c=sqrt%28160sin%28100%5Eo%29%2Fsin%2850%5Eo%29%29\"$ ---> $\"c=14.342\"$ (rounded) \n" ); document.write( "

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