In triangle ABC, height CH = 3, side AB = 6 and angle ∠BAC = 75∘ Find angle ∠ABC

The solution of the problem:

1. Consider the triangle ANC.

tg 750 = CN: AN;

AN = CN: tg 750;

AN = 3: 3.732;

AN = 0.8.

2.. Consider the NBC triangle. Let’s define the NB side.

NB = AB – AN;

NB = 6 – 0.8 = 5.2.

Let’s define the angle ABC.

tg ABC = NC: NB;

tg ABC = 3: 5.2;

tg ABC = 0.577;

angle ABC = 300.

Answer: Angle ABC of triangle ABC is 300.