The two angles of the triangle are 63 and 27 degrees. Find the angle between the height

The two angles of the triangle are 63 and 27 degrees. Find the angle between the height and the median, drawn from the top of the third corner.

Let ΔABС be given. The two angles of the triangle are ∠A = 63 ° and ∠B = 27 °, so the third ∠C = 180 ° – (63 ° + 27 °) = 90 °, since the sum of the angles in the triangle is 180 °.
The height of the CК and the median of the CM are drawn from the apex of the third angle. The height divides ΔАВС into two right-angled triangles ΔАСК and ΔВСК (∠К = 90 °), then ∠KСВ = 90 ° – 27 ° = 63 °, since the sum of acute angles in a right-angled triangle is 90 °.
Point M is the center of the circumscribed circle, which means that ΔMСB is an isosceles triangle with base CB. By the property of angles at the base of an isosceles triangle: ∠MСВ = ∠MBC = 27 °.
The angle between the height and the median is ∠KСM = ∠KСВ – ∠MСВ = 63 ° – 27 ° = 36 °.
Answer: the angle between the height and the median is 36 °.