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

1. Since AC = 6 conventional units and BC = 8 conventional units – legs, then AB – hypotenuse (since it lies opposite an angle equal to 90 degrees). By the Pythagorean theorem:
AB = √ (AC ^ 2 + BC ^ 2);
AB = √ (6 ^ 2 + 8 ^ 2) = √ (36 + 64) = √100 = 10 (conventional units).
2. CК – the median drawn to the hypotenuse from the right angle. From the properties of a right-angled triangle, it is known that the median drawn from a right angle to the hypotenuse is equal to half of the hypotenuse. Then:
CK = AB / 2;
CK = 10/2 = 5 (conventional units).
Answer: CК = 5 conventional units.