The angle between the height of a right-angled triangle, lowered to the hypotenuse, and one of the legs

The angle between the height of a right-angled triangle, lowered to the hypotenuse, and one of the legs is 60 degrees. The second leg is 12 cm. Find the hypotenuse.

Let us designate this right-angled triangle ABC, height CH, angle HCB = 60 °, leg AC = 12 cm.
Consider a right-angled triangle ВСН, in it, according to the condition, the angle НСВ = 60 ° is known, which means that the second acute angle НВС = 90 ° – 60 ° = 30 °.
Opposite the acute angle B = 30 ° in the right-angled triangle ABC, the leg AC = 12 cm is located.
This means that the hypotenuse AB = 2 * AC = 2 * 12 = 24 (cm).
Answer: the length of the hypotenuse AB is 24 cm.