SOLUTION: In triangle ABC, the measure of angle A equals {{{ x^2+12 }}}, the measure of angle B equals {{{ 11x+5 }}} and the measure of angle C equals {{{ 13x-17 }}}. Determine the longest s

Algebra ->  Triangles -> SOLUTION: In triangle ABC, the measure of angle A equals {{{ x^2+12 }}}, the measure of angle B equals {{{ 11x+5 }}} and the measure of angle C equals {{{ 13x-17 }}}. Determine the longest s      Log On


   

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.
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
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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A:
m∠A + m∠B + m∠C = 180°
+%28x%5E2%2B12%29+%2B+%2811x%2B5%29+%2B+%2813x-17%29+=+180+
+x%5E2%2B+24x+-+180+=+0+
(x - 6)(x + 30) = 0
x = 6, disregard x = -30 because it will make some angles negative
m∠A = +6%5E2%2B12+ = 48°
m∠B = 11(6) + 5 = 71°
m∠C = 13(6) - 17 = 61°
The longest side is opposite the largest angle.
The largest angle is ∠B and the side opposite ∠B is AC.
Therefore, the longest side is AC.