In a right-angled triangle ABC, angle C is 90 degrees, CD is the height of the triangle, AC = 8cm, CB = 6cm. Find CD Length

Since C = 90 °, the triangle is right-angled, we calculate the hypotenuse AB, by the Pythagorean theorem we get:

AB ^ 2 = AC ^ 2 + CB ^ 2 = 8 ^ 2 + 6 ^ 2 = 100 cm.

AB = √100 = 10 cm.

Find the area of the triangle:

1/2 * AB * AC = 1/2 * 6 * 8 = 24 cm ^ 2.

On the other hand, the area is equal to 1/2 of the height times the hypotenuse:

1/2 * AB * CD = S;

CD = 2S / AB = 2 * 24/10 = 4.8 cm.

Answer: The height of triangle CD is 4.8cm.