In a right-angled triangle, the legs are 20 cm and 15 cm. Find the height of the triangle drawn to the hypotenuse.

1. Let’s introduce the designations of the vertices of the triangle ABC. AH – the height drawn to the hypotenuse BC.
The apex angle A is 90 °.
2. We calculate the length of the hypotenuse of the BC:
ВС = √АВ ^ 2 + АС ^ 2 = √20 ^ 2 + 15 ^ 2 = √625 = 25 cm.
3. We calculate the area S of the triangle using Heron’s theorem:
S = √30 (30 – 20) (30 – 15) (30 – 25) = √30 x 10 x 5 x 15 = √22500 = 150 cm ^ 2.
3. Calculate the height AH using a different area formula:
S = BC x AH / 2;
AH = 2 x S / 25 = 300/25 = 12 cm.
Answer: the height drawn to the hypotenuse is 12 cm.