In a right-angled triangle with legs 12 and 16 cm, find the height drawn from the top of the right angle.

First, we find the length of the hypotenuse by the Pythagorean theorem.

c = √ (144 cm² + 256 cm²) = √400 cm² = 20 cm.

The height drawn from the top of the right angle divides the hypotenuse into 2 segments. Let’s find the length of one segment along the hypotenuse and the adjacent leg.

n = 144 cm² ÷ 20 cm = 7.2 cm.

The height also divides the triangle into 2 right-angled triangles, in which it is the leg. Let’s find it by the Pythagorean theorem.

h = √ (144 cm² – 51.84 cm²) = √92.16 cm² = 9.6 cm.

Answer: the height is 9.6 cm.