Find the height of a right-angled triangle, lowered by the hypotenuse, if its legs are 12 cm and 5 cm.

By the Pythagorean theorem, the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse. Let’s find the hypotenuse:

c ^ 2 = a ^ 2 + b ^ 2 = 12 ^ 2 + 5 ^ 2 = 144 + 25 = 169 = 132;

c = 13 cm.

The area of a right-angled triangle can be found as half the product of the legs:

S = 0.5 * a * b = 0.5 * 12 * 5 = 30 cm2.

On the other hand, the area of the same triangle is equal to half the product of the hypotenuse and the height drawn to the hypotenuse. Knowing the value of the area and hypotenuse, we can find the height:

S = 0.5 * c * h;

h = 2 * S / c = 2 * 30/13 = 60/13 ≈ 4.62 cm – the height lowered to the hypotenuse.