In triangle ABC, angle C = 90 degrees, angle B = 30 degrees BC = 12√3. Find the length medians BM.

Through the leg and the acute angle, we determine the length of the second leg of the right-angled triangle ABC.

tgABC = AC / BC.

AC = BC * tg30 = 12 * √3 * (1 / √3) = 12 cm.

Since, by condition, BM is the median of the triangle ABC, then AM = CM = AB / 2 = 12/2 = 6 cm.

In the right-angled triangle of the BCM, according to the Pythagorean theorem, we determine the length of the hypotenuse of the BM.

BM ^ 2 = BC ^ 2 + CM ^ 2 = (12 * √3) ^ 2 + 6 ^ 2 = 423 + 36 = 468.

BM = √468 = 6 * √13 cm.

Answer: The length of the median BM is 6 * √13 cm.