In a right-angled triangle ABC, angle C is 90 degrees, angle A is 40 degrees.

In a right-angled triangle ABC, angle C is 90 degrees, angle A is 40 degrees. Find the angle between the median and the height drawn from vertex C.

The ACK triangle, formed by the median СK, is isosceles, AK = СK by the property of the median drawn to the hypotenuse, then the angle ACK = CAK = 40.

The ACH triangle is rectangular, since CH is the height of the ABC triangle, then the angle ACH = (90 – CAH) = (90 – 40) = 50.

Then the angle КСH = АСH – АСК = 50 – 40 = 10.

Answer: The angle between the height and the median is 10.