In triangle ABC, angle A is 80 degrees, angle B is 70 degrees. The large side is 5 cm. A) What are the larger

In triangle ABC, angle A is 80 degrees, angle B is 70 degrees. The large side is 5 cm. A) What are the larger and smaller sides of the triangle (justify the answer). b) Calculate the smaller side of the triangle.

a) The large side BC lies against the larger angle A = 80, the smaller AB – against the angle C = 180 – (80 + 70) = 30 degrees.

b) The height CM is drawn in the triangle ABC. In the triangle CMB CM = BC * sin B. In the triangle CMA AC = CM / sin A = BC * sin B / sin A.

The height AK is drawn in the triangle ABC. In the triangle AKC AK = AC * sin C = (BC * sin B / sin A) * sin C. In the triangle AKB AB = AK / sin B = (BC * sin B / sin A) * sin C / sin B = BC * sin C / sin A.

So, AB = 5 * 0.5 / 0.985 = 2.54 cm.