In a right-angled triangle, a median and a bisector were drawn from the vertex of the right angle.

In a right-angled triangle, a median and a bisector were drawn from the vertex of the right angle. The angle between them turned out to be 11 °. Find the smallest angle of the triangle.

Since BН, by condition, is the bisector of the right angle, then the angle ABN = СBН = 90/2 = 45.

Then the angle СBМ = СBН + МBН = 45 + 11 = 56.

Angle ABM = ABC – CBM = 90 – 56 = 34.

By the property of the median drawn to the hypotenuse from the vertex of the right angle, BM = AC / 2 = AM = CM, then the triangle ABM is isosceles, and then the angle BAM = ABM = 34.

Angle АСВ = 90 – 34 – 56.

Answer: The smallest angle of a triangle is 34.