In a rectangular triangle ABC, angle C = 90 degrees, angle B = 30 degrees, BC = 18 cm, CK

In a rectangular triangle ABC, angle C = 90 degrees, angle B = 30 degrees, BC = 18 cm, CK is the height drawn to the AB side, KM is the perpendicular drawn from point K to the BC side. What is the length of the MB?

Since the CК is the height of the ABC triangle, then the BCK triangle is rectangular, in which the SC leg is located opposite the angle 300, then CК = BC / 2 = 18/2 = 9 cm.

Let us determine the length of the leg ВK in the right-angled triangle ВCK using the Pythagorean theorem.

ВK ^ 2 = BC ^ 2 – СK ^ 2 = 324 – 81 = 243.

BK = √243 = 9 * √3 cm.

In a right-angled triangle of the ВМК, we determine the length of the ВM leg.

Cos30 = BM / BK.

BM = BK * Cos30 = 9 * √3 * √3 / 2 = 13.5 cm.

Answer: The length of the BM segment is 13.5 cm.