The legs of a right triangle are 35 and 120, find the height drawn to the hypotenuse.

Let’s find the area of a right-angled triangle, if, by condition, we know its legs:
S = 1/2 * a * b = 1/2 * 35 * 120 = 2100.
The area of a right triangle can be found through the hypotenuse and the height drawn to it. We know the area, we find the hypotenuse by the Pythagorean theorem. Let’s use the area formula and find the height.
c = √ (a² + b²) = √ (35² + 120²) = √ (1225 + 144400) = √15625 = 125.
S = 1/2 * c * h
2S = c * h
h = 2S / c = 2 * 2100/125 = 33.6.
Answer: height 33.6.