The height of the rectangular triangle, lowered to the hypotenuse, forms an angle of 55 (degrees)

The height of the rectangular triangle, lowered to the hypotenuse, forms an angle of 55 (degrees) with one of the legs. Find the acute angles of this triangle.

Let ABC be a right-angled triangle, ygo B = 90 degrees, BH – height, angle СBH = 55 degrees.
1. Consider a triangle BHC: angle СBН = 55 degrees (by condition), angle BНС = 90 degrees (since ВН – height, ie perpendicular). By the theorem on the sum of the angles of a triangle, we find the angle НСB:
angle СBН + angle BНС + angle НСB = 180 degrees;
55 + 90 + angle НСВ = 180;
angle НСВ = 180 – 145;
angle НСВ = 35 degrees.
Angle angle НСВ = angle С = 35 degrees.
2. Consider a triangle ABC: angle B = 90 degrees (by condition), angle C = 35 degrees. By the theorem on the sum of the angles of a triangle, we find the angle A:
angle A + angle B + angle C = 180 degrees;
angle A + 90 + 35 = 180;
angle A = 180 – 125;
angle A = 55 degrees.
Answer: angle A = 55 degrees, angle C = 35 degrees.