In a right-angled triangle ABC with a right angle C, legs AC = 6, BC = 8 are known. find the median CK of this triangle.

1. Side AB in a right-angled triangle ABC is the hypotenuse.

2. Considering that, according to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse, we calculate its length:

AC ^ 2 + BC ^ 2 = AB ^ 2;

8 ^ 2 + 6 ^ 2 = AB ^ 2;

AB = √64 + 36 = √100 = 10.

3. Taking into account that the median drawn from the right angle to the hypotenuse is equal to 1/2 of the hypotenuse, we calculate what the length of the median CK is equal to:

10: 2 = 5.

Answer: The median CK is 5.