In a right-angled triangle, one of the sharp corners is 4 times the size of the other.

In a right-angled triangle, one of the sharp corners is 4 times the size of the other. Find the angle between the median and the height drawn from the vertex of the right angle.

Let the value of the angle BAC = X0, then, by condition, the angle BCA = 4 * X0.

In a right-angled triangle, the sum of the acute angles is 90.

X + 4 * X = 90.

X = 90/5 = 18.

BAC angle = 18, BCA angle = 18 * 4 = 72.

In a right-angled triangle ВСН, the angle СВН = 90 – 72 = 18.

Since BM is the median, its length is equal to half the length of the hypotenuse, which means that the triangle BAM is isosceles, since BM = AM, then the angle ABM = BAM = 18.

Angle MВM = 90 – СВН – AВM = 90 – 18 – 18 = 58.

Answer: The angle between the height and the median is 58.