The shortest side of a triangle is 4.3m long. Two of the angles are 45.1 and 51.2 degrees respectively. Find the length of the longest side.

To begin we calculate the third unknown angle in the triangle by taking the two known angles (45.1 and 51.2) away from 180 degrees (remember the interior angles of a triangle sum to 180). We find this angle to be 83.7. As the question states the shortest side is 4.3m, we can tell that this must be opposite the smallest angle in the triangle. Now draw a sketch of the triangle to help visualise. Now we know 1 side length and 3 angles. We can now use the sine rule [(sin(A)/a=sin(B)/b] to solve. The question asks for the longest side length, so this must be the side opposite the largest angle (83.7). So by substituting A=83.7, B=45.1 and b=4.3 into the sine rule equation we can calculate the longest side length 'a'. We get a to be 6.03 correct to 2 d.p.

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