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

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

Let the length of the segment BM = X cm.

In a right-angled triangle BKM, tgMBK = MK / BM.

MK = BM * tg30 = X * √3 / 3 cm.

The length of the segment CM = BC – BM = (18 – X) cm.

Rectangular triangles BMK and CBM are similar in acute angle.

Then their similarities are triangles, BM / MK = MK / CM.

X / (X * √3 / 3) = (X * √3 / 3) / (18 – X).

X * (18 – X) = X ^ 2/3.

X – 54 + 3 * X = 0.

4 * X = 54.

X = MB = 54/4 = 13.5 cm.

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