The height of a right-angled triangle divides the right angle into 2 angles, one of which

The height of a right-angled triangle divides the right angle into 2 angles, one of which is 4 times larger than the other. Find the sharp corners of this triangle.

The height of a right-angled triangle, drawn from the vertex of the right angle, divides the ABC triangle into two similar triangles, each of which is similar to the original one. Let the value of the angle СBН = X0, then the angle АBН, by condition, is equal to 4 * X0.

Then the angle СBН = BAC = X0.

Angle ABC = BCA = 4 * X0.

BAC + ABC + BCA = X + 5 * X + 4 * X = 180.

10 * X = 180.

СBН = BAC = 180/10 = 18.

ABC = BCA = 4 * 18 = 72.

Answer: The acute angles of the triangle ABC are 18 and 72.