The angle between the bisector and the height drawn from the vertex of the largest angle of a right

The angle between the bisector and the height drawn from the vertex of the largest angle of a right triangle is 14 degrees. Find the angles of the triangle

Let us designate this right-angled triangle ABC, angle B – straight line, BH – height, BK – bisector of angle B, angle KBH = 14 °.
In the KBC triangle, the angle KBC = 45 ° (BK is the bisector).
We find the angle НВС:
∠ HBC = ∠ KBC – ∠KBH = 45 ° – 14 ° = 31 °.
In a right-angled triangle НBC, one acute angle is found, we find the angle С:
∠ С = 90 ° – ∠ HBC = 90 ° – 31 ° = 59 °.
Find the second acute angle A in the right-angled triangle ABC:
∠ А = 90 ° – ∠ С = 90 ° – 59 ° = 31 °.
Answer: the acute angles of the triangle ABC are equal to 31 ° and 59 °.