In a right-angled triangle, the angle between the height and the bisector drawn from the vertex of the right

In a right-angled triangle, the angle between the height and the bisector drawn from the vertex of the right angle is 12 degrees. Find the degree measure of the smaller angle of this triangle.

1. Let us introduce the designation of the vertices of the triangle by the symbols A, B, C. Angle C = 90 °. Angle KCH = 12 °.

СН – height, СK – bisector. Point K is on the side AB between points H and B.

2. Angle ВСK = 90 °: 2 = 45 °, since the bisector CК divides the right angle С into two equal parts.

3. Angle АСН = 45 ° – 12 ° = 33 °.

4. Angle AНС = 90 °, since CH is the height. Angle A = 180 ° – 33 ° – 90 ° = 57 °.

5. Angle B = 180 ° – 57 ° – 90 ° = 33 °.

Answer: the smaller angle of the triangle ABC is the angle B, equal to 33 °.