Find the median AM of a right-angled triangle ABC if the hypotenuse of AB is 5 and the coset of AC is 3.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the leg BC.

BC ^ 2 = AB ^ 2 – A ^ C2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16.

BC = 4 cm.

Since the segment AM is the median of the triangle ABC, then CM = BM = BC / 2 = 4/2 = 2 cm.

In a right-angled triangle AFM, according to the Pythagorean theorem, we determine the length of the hypotenuse AM.

AM ^ 2 = AC ^ 2 + CM ^ 2 = 3 ^ 2 + 2 ^ 2 = 9 + 4 = 13.

AM = √13 cm.

Answer: The length of the median AM is √13 cm.