In a right-angled triangle ABC, angle C = 90 (degrees), angle B = 30 (degrees)

In a right-angled triangle ABC, angle C = 90 (degrees), angle B = 30 (degrees), BC = 18 cm, CK is perpendicular to AB, KM is perpendicular to BC. Find MB.

The ACK triangle is rectangular, since the CK is perpendicular to AB, the CK leg lies opposite the angle 30, then its length is equal to half the length of the BC hypotenuse. CK = BC / 2 = 18/2 = 9 cm.

In a right-angled triangle BKM, the angle BKM = (90 – 30) = 60, then in a right-angled triangle CMK, the angle CKM = (90 – 60) = 30.

The CM leg lies against an angle of 30, then CM = CK / 2 = 9/2 = 4.5 cm.

Then BM = BC – CM = 18 – 4.5 = 13.5 cm.

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