In triangle ABC, angle C = 90 degrees, sine A = 7/36, AB = 144. Find BC.

Given:

ABC – right triangle;

Angle C = 90 °;

AB = 144;

sin A = 7/36;

Find BC.

Decision:

The ratio of the opposite leg BC to the hypotenuse AB is equal to the cosine of angle A.

So we get: cos A = BC / AB;

Hence, BC = AB * cos a;

Substitute the known values into the formula and find BC.

BC = 144 * 7/36 = 12 * 12 * 7 / (12 * 3) = 1 * 12 * 7 / (1 * 3) = 12 * 7/3 = 12/3 * 7 = 4 * 7 = 28;

As a result, we got BC = 28.

Answer: BC = 28.