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

In a right-angled triangle, the angle between the height and the bisector drawn from the vertex of the right angle is 37 degrees. Find the smaller angle of the given triangle.

1. Let us introduce the designation of the vertices of the triangle by the symbols A, B, C. Angle C = 90 °. КСН angle = 37 °.

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

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

3. Angle АСН = 45 ° – 37 ° = 8 °.

4. Angle AНС = 90 °, since CH is the height. Angle A = 180 ° – 8 ° – 90 ° = 82 °.

5. Angle B = 180 ° – 82 ° – 90 ° = 8 °.

Answer: the smaller angle of the triangle ABC is the angle B, equal to 8 °.