# Solve a triangle, 2 sides are given.

Jun 8th, 2016
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Given triangle ABC with AB=6, AC=9, find BC

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ProblemGiven triangle ABC with AB=6, AC=9, find BCSolutionDraw a sketch as shown in the figure.Let x = length of BC.From the Law of Sines, the area of the triangle is1Area = ( 6 )( 9 ) sin = 27 sin 2From the Law of Cosines, obtainx 2 = 92 + 62 2 ( 9 )( 6 ) cos = 117 108cos cos =117 x 2108 117 x 2 sin = 1 108 2The area may also be calculated by using Herons formula.a = x, b = 9, c = 611x + 15s = (a + b + c) = (6 + 9 + x) =222x + 1515 xsa =x=22x + 15x 3s b =9 =22x + 15x+3

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