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

Find the length of the hypotenuse of a right-angled triangle:

AB² = AC² + BC² = 6² + 8² = 36 + 64 = 100.

AB = √100 = 10.

Consider triangles ABC and СНВ: angle B is common, they are both rectangular, which means that triangle ABC is similar to triangle СНВ.

Let us express the coefficient of similarity: СВ / AB = CH / AC;

8/10 = CH / 6.

CH = 8 * 6: 10 = 48: 10 = 4.8.

Answer: CH height is 4.8.