In triangle ABC: angle C = 90 degrees, angle B = 30 degrees. AC = 6 cm, find the length of the median BM.

1. We calculate the length of the hypotenuse AB of the right-angled triangle ABC using its property

about the fact that the AC leg, located opposite an angle of 30 °, is equal to half of the hypotenuse:

AB = AC x 2 = 6 x 2 = 12 cm.

2. Calculate the length of the BC leg. For the calculation, we use the Pythagorean theorem:

ВС = √АВ² – АС² = √12² – 6² = √144 – 36 = √108 = 6√3 cm.

3. We calculate the length of the median BM, which in the right-angled triangle of the BCM is

hypotenuse. For the calculation, we also use the Pythagorean tower:

ВM = √BC² + CM².

CM = AC: 2 = 6: 2 = 3 cm (the median BM divides the side to which it is drawn into two

identical segments).

BM = √ (6√3) ² + 3² = √108 + 9 = √117 = 3√13 cm.

Answer: the length of the median BM is 3√13 cm.