Work out the area of this triangle given the lengths of 1 sides (a) and 2 angles (A and B) using either the sine rule

We know the area of any triangle is equal to 0.5abSin(C). This means we need to find the length of side b and the angle C.First we can work out the angle C of the triangle as we know the angles in a triangle add up to 180 degrees. Say we have angle A is 35 and angle B is 70. This means angle C is 180 - (35 + 70). Next we can use the sine rule to calculate the value of side b. Say side a = 5cm. The rule is a/Sin(A) = b/Sin(B) = c/Sin(C). Substituting in the values we have we can say 5/Sin35 = b/Sin70. Rearrange to get b = 5Sin70/Sin35.
Therefore the area of the triangle = 0.5 * 5 * 5sin70/sin35 * sin 75