In a right-angled triangle, one leg is 10 dm, and the hypotenuse is 26 dm. find the second leg

In a right-angled triangle, one leg is 10 dm, and the hypotenuse is 26 dm. find the second leg and the height lowered to the hypotenuse.

By the Pythagorean theorem, we determine the length of the leg AB.

AB ^ 2 = AC ^ 2 – BC ^ 2 = 676 – 100 = 576.

AB = 24 dm.

Let us prove that right-angled triangles ABC and BCH are similar.

Let the angle BAC = X0, then in the triangle ABH the angle ABH = (90 – X) 0.

In the СBН triangle, the angle СBН = СBА – АВН = (90 – (90 – X) = X0.

Angle СBН = BAC, therefore, right-angled triangles ABC and ВСН are similar in acute angle.

Then AC / AB = BC / BH.

BH = AB * BC / AC = 24 * 10/26 = 240/26 = 120/13 = 9 (3/13) dm.

Answer: The second leg is 24 dm, the height is 9 (3/13) dm.