In triangle ABC AB = 7, sinA = 1 \ 5, sinC = 1 \ 6 Find BC.

If a side and two angles are known in a triangle, then the unknown side can be found by

sine theorem. The ratio of the side of a triangle to the sine of the angle opposite

it, for a given triangle – the value is constant.

AB / sin C = BC / sin A; AB = 7; sin A = 1/5; sin C = 1/6;

BC = AB * sin A: sin C = 7 * 1/5: 1/6 = 42/5 = 8.4.