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 7 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 °. Angle KCН = 7 °.

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

2. The angle BCK = 90 °: 2 = 45 °, since the bisector CK divides the right angle C into two equal parts.

3. Angle ACН = 45 ° – 7 ° = 38 °.

4. Angle АНC = 90 °, since CH – height. Angle A = 180 ° – 38 ° – 90 ° = 52 °.

5. Angle B = 180 ° – 52 ° – 90 ° = 38 °.

Answer: the smaller angle of the triangle ABC is the angle B, equal to 38 °.