In a right-angled triangle ABC, angle B = 90 *, AB = 8cm, AC = 16cm.

In a right-angled triangle ABC, angle B = 90 *, AB = 8cm, AC = 16cm. Find the angles that form the height of the BH with the legs of the triangle.

1. Considering that, according to the properties of a right-angled triangle, the ratio of the leg AB to the hypotenuse AC is the sine of the angle at the vertex C, we calculate the value of this angle.

Sine of angle C = AB / AC = 8/16 = 1/2. Angle A = 30 °.

2. We calculate the value of the angle СBН between the height BН and the leg ВС of the triangle ABC:

angle СBН = 180 – 30 ° – 90 ° = 60 °.

3. We calculate the value of the angle ABH formed by the height BH and the leg AB of the triangle ABC:

angle ABH = 90 ° – 60 ° = 30 °.

Answer: angle СBН = 60 °, angle АBН = 180 ° – 60 ° = 30 °.