In a right-angled triangle ABC, the angle is C = 90 degrees, AB = 10cm, BC = 5cm. Find the angles

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

AB is the hypotenuse, BC is the leg opposite <A. Our leg BC is 2 times less than the hypotenuse AB. We know that the leg opposite the 30 degree angle is half the hypotenuse. Therefore, <A = 30 degrees.

In the AСН triangle: <H = 90 degrees, <A = 30 degrees. We know that the angles of a triangle add up to 180 degrees. <A + <C + <H = 180; <C = 180 – <A – <H = 180 – 30 – 90 = 60 degrees.

<ACB = <ACН + <BCH; <BCH = <ACB – <ACН; <BCH = 90 – 60 = 30.

The height divides angle C into two angles of 30 degrees and 60 degrees.