The legs of a right-angled triangle are 10 and 24. Find the height drawn to the hypotenuse.

Let us denote the length of the height drawn to the hypotenuse in a given right-angled triangle by h.
Using the Pythagorean theorem, we find the hypotenuse from a given right-angled triangle:
c = √ (10 ^ 2 + 24 ^ 2) = √ (100 + 576) = √676 = 26.
Since the leg in a right-angled triangle is also the height of this right-angled triangle, drawn to the other leg, the area S of a right-angled triangle is half the product of the lengths of the legs:
S = 10 * 24/2 = 120.
At the same time, the area of ​​a right-angled triangle is equal to half the product of the length of the hypotenuse and the height drawn to the hypotenuse of this right-angled triangle, therefore, the following relationship is true:
h * 26/2 = 120.
We solve the resulting equation:
h * 13 = 120;
h = 120/13;
h = 9 3/13.

Answer: The length of the height drawn to the hypotenuse is 9 3/13. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.