The leg and hypotenuse of a right triangle are equal to 21 and 35. Find the height drawn to the hypotenuse.

By the Pythagorean theorem, we can find the square of the second leg of a given right-angled triangle:

a ^ 2 = 35 ^ 2 – 21 ^ 2 = 1225 – 441 = 784;

a = √784 = 28 – the second leg.

The area of a right-angled triangle is half the product of the legs:

S = 0.5 * 21 * 28 = 294.

On the other hand, the area of this triangle is half the product of the hypotenuse and the height drawn to it:

S = 0.5 * c * h.

Hence, the height drawn to the hypotenuse:

h = 2 * S / c = 2 * 294/35 = 588/35 = 16.8.