In a right-angled triangle, the angle is C = 90 °, AB = 10 cm, BC = 5 cm.

In a right-angled triangle, the angle is C = 90 °, AB = 10 cm, BC = 5 cm. Find the angles by which the height CH divides the angle C.

In a right-angled triangle ABC, side AB is the hypotenuse, BC is the leg.
BC / AB = 5/10 = 1/2
Hence, in accordance with the properties of the leg of a right-angled triangle, the angle A = 30 °.
Then in the triangle ANC we know 2 angles: the angle H = 90 ° (since CH is the height) and the angle A = 30 °.
Then the angle C = 180-90-30 = 60 °.
The remaining angle C, belonging to the CNB triangle, is 90-60 = 30 °.