In a right triangle, the angle between the hypotenuse and the median to it is 76 degrees

In a right triangle, the angle between the hypotenuse and the median to it is 76 degrees. Find the larger of the two acute corners of the right triangle.

Since triangle ABC is rectangular, and CM is the median drawn to the hypotenuse, the length of the median is equal to half the length of the hypotenuse. CM = AB / 2 = BM, then the BCM triangle is isosceles, then the angle MCB = MBC = (180 – BMC) / 2 = (180 – 76) / 2 = 52.

Angle BAC = (90 – 52) = 38.

Answer: The larger acute angle is 52.