The larger of the two acute angles of a right triangle is 71 degrees. Find the degree measure of the angle

The larger of the two acute angles of a right triangle is 71 degrees. Find the degree measure of the angle between the height and the bisector drawn from the apex of the right angle.

Since AM is a bisector drawn from the vertex of a right angle, the angle BAM = CAM = 90/2 = 45.

AH is the height of the ABC triangle, then the ACH triangle is rectangular, and the angle CAН = 180 – 90 – 71 = 19.

Then the angle between the bisector AM and the Height AH will be equal to: MAН = CAM – СAН = 45 – 19 = 26.

Answer: The angle between the height and the bisector is 26.