The height drawn from the top of the right angle of the triangle divides the hypotenuse into segments equal to 5cm

The height drawn from the top of the right angle of the triangle divides the hypotenuse into segments equal to 5cm and 15cm, which is equal to the smaller leg of the triangle.

Segments BD and DC – projections of legs AB and AC on the hypotenuse. The smaller AC leg has a smaller projection DC = 5 cm.

BC = BD + DC = 15 + 5 = 20 cm.

Triangles ABC and ADB are rectangular. They have a common angle C. If the acute angle of one right-angled triangle is equal to the acute angle of the other, then they are similar.

From the similarity of triangles it follows:
AC / BC = DC / AC (for both triangles, the ratio of the leg to the hypotenuse; leg in both cases is adjacent to <C).

AC ^ 2 = BC * DC = 20 cm * 5 cm = 100 cm ^ 2;

AC = √ (100 cm ^ 2) = 10 cm.

Answer: 10 cm.