In a right-angled triangle ABC, angle C is straight, AC = 4cm, CB = 4 √3cm, CM is the median. Find the BCM angle.

Let us determine, by the Pythagorean theorem, the length of the hypotenuse AB.

AB ^ 2 = AB ^ 2 + BC ^ 2 = 16 + 48 = 64.

AB = 8 cm.

Since CM is the median drawn from the vertex of the right angle to the hypotenuse, its length is equal to half the length of the hypotenuse.

CM = BM = AM = AB / 2 = 8/2 = 4 cm.

Then, in the ACM triangle, the lengths of all sides are equal, AC = AM = CM = 4 cm, the triangle is equilateral, and all its internal angles are 60.

Then the angle ВСМ = 90 – 60 = 30.

Answer: The BCM angle is 30.