# ABC is a triangle with sides of length AB, 12m and BC,14m. Angle ACB = 43 degrees. Find the area of the triangle.

Use of the Sine Rule to ultimately work out the area of a triangleA/SinA = B/SinB14/Sin43 = 12/SinX14SinX = 12Sin43SinX = 12Sin43/14X=InverseSin(12Sin43/14) = 35.77-There are 180 degrees in triangle. Therefore, to work out the remaining angle we must subtract the two known angles from 180 degrees. Remaining angle = 180 – 35.77 – 43                                                           = 101.2273801 =101.23-As we know the angle and the lengths of the two sides between them we can work out the area of the triangle using the following formula, A= 0.5ABsinCTherefore, A = 0.5 x 12 x 14 x sin (101.2273801)                         = 82.39 m2

Answered by Eoin C. Maths tutor

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