document.write( "Question 830177: In triangle ABC, the measure of angle A equals $\"+x%5E2%2B12+\"$ , the measure of angle B equals $\"+11x%2B5+\"$ and the measure of angle C equals $\"+13x-17+\"$ . Determine the longest side of triangle ABC. \n" ); document.write( "

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Q:
\n" ); document.write( "In triangle ABC, the measure of angle A equals $\"+x%5E2%2B12+\"$ , the measure of angle B equals $\"+11x%2B5+\"$ and the measure of angle C equals $\"+13x-17+\"$ . Determine the longest side of triangle ABC.
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\n" ); document.write( "A:
\n" ); document.write( "m∠A + m∠B + m∠C = 180°
\n" ); document.write( " $\"+%28x%5E2%2B12%29+%2B+%2811x%2B5%29+%2B+%2813x-17%29+=+180+\"$
\n" ); document.write( " $\"+x%5E2%2B+24x+-+180+=+0+\"$
\n" ); document.write( "(x - 6)(x + 30) = 0
\n" ); document.write( "x = 6, disregard x = -30 because it will make some angles negative
\n" ); document.write( "m∠A = $\"+6%5E2%2B12+\"$ = 48°
\n" ); document.write( "m∠B = 11(6) + 5 = 71°
\n" ); document.write( "m∠C = 13(6) - 17 = 61°
\n" ); document.write( "The longest side is opposite the largest angle.
\n" ); document.write( "The largest angle is ∠B and the side opposite ∠B is AC.
\n" ); document.write( "Therefore, the longest side is AC. \n" ); document.write( "

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