The legs of a right-angled triangle are 21 and 28. Find the height drawn to the hypotenuse.

The sum of the squares of the legs is equal to the square of the hypotenuse, we find the square of the hypotenuse of this triangle:
21 ^ 2 + 28 ^ 2 = 441 + 784 = 1225.
The hypotenuse is √1225 = 35.
The area of a right-angled triangle is equal to half the product of the legs: S = 0.5 * 21 * 28 = 294.
On the other hand, the area of the same triangle can be defined as half of the product of the hypotenuse and the length of the height drawn to it: S = 0.5 * h * 35. From here we can find the height drawn to the hypotenuse: h = 2S / 35 = 2 * 294/35 = 16.8.
The desired height is 16.8.