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

The largest of the 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.

The bisector divides the right angle in half, which means the angle between the height and the bisector is equal to the difference of 45 ° and the angle between the height and the leg of the triangle. We calculate this angle from a right-angled triangle, in which one acute angle is 71 °, so the second acute angle is 90 ° – 71 ° – 19 °.

Therefore, the sought angle between the bisector and the height is:

45 ° – 19 ° = 26 °.