The angle between the bisector and the height emanating from the vertex of the right angle

The angle between the bisector and the height emanating from the vertex of the right angle is 24 degrees. Find the smaller angle of the triangle.

Suppose that in triangle ABC the value of the angle ACB is 90 °, CH is the height of the triangle drawn from the vertex of the right angle to the hypotenuse AB, СК is the bisector of the right angle. It is known that the angle between the bisector and the height emanating from the vertex of the right angle is 24 degrees, that is, the НСК angle = 24 °. To find the smaller angle of the CAB triangle, consider first Δ НCК. In it, the angle NCК = 24 ° by condition, the angle СНK = 90 °, since CH is the height, which means that the angle СKН = 90 ° – 24 ° = 66 °, then the additional angle СKA = 180 ° – 66 ° = 114 °. In Δ AKС, the angle KСA = 90 °: 2 = 45 °, then the angle НAO = 180 ° – (114 ° + 45 °) = 21 °, since the sum of the angles in the triangle is 180 °, then the smaller angle of the triangle CAB = 21 ° …
Answer: the smaller angle of the triangle CAB = 21 °