document.write( "Question 733518: the measure of two angles are 100 degrees and 46 degrees. the length of the shortest sides of the triangle is 12. find the measure to the nearest integer and the lengths of the other two sides \n" ); document.write( "

Algebra.Com's Answer #448477 by KMST(5328) $\"\"$ $\"About$

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The measures of two angles of a triangle are $\"100%5Eo\"$ and $\"46%5Eo\"$ .
\n" ); document.write( "We know that the measures of all 3 angles add up to $\"180%5Eo\"$ , so the measure of the third angle is
\n" ); document.write( " $\"180%5Eo-%28100%5Eo%2B46%5Eo%29=180%5Eo-146%5Eo=34%5Eo\"$
\n" ); document.write( "In a triangle, the shortest side is opposite the smallest angle and the longest side is opposed the largest angle, so the shortest side is opposite the $\"34%5Eo\"$ angle.
\n" ); document.write( "The law of sines, says that in a triangle the ratio of the length of a side and the sine of the opposite angle is constant.
\n" ); document.write( "That means that the lengths, a, and b of the other two sides are related by
\n" ); document.write( " $\"12%2Fsin%2834%5Eo%29=a%2Fsin%28100%5Eo%29=b%2Fsin%2846%5Eo%29\"$
\n" ); document.write( "Using approximate values for the sines of those angles.
\n" ); document.write( " $\"12%2F0.559=a%2F0.985=b%2F0.719\"$
\n" ); document.write( "Solving the equations that can be split from there,
\n" ); document.write( " $\"12%2F0.559=a%2F0.985\"$ --> $\"12%2F0.559%2A0.985=a\"$ --> $\"highlight%28a=21.1%29\"$ (rounded)
\n" ); document.write( " $\"12%2F0.559=b%2F0.719\"$ --> $\"12%2F0.559%2A0.719=b\"$ --> $\"highlight%28b=15.4%29\"$ (rounded) \n" ); document.write( "

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