In a right-angled triangle ABC, the leg AC = 55, and the height of the CH

In a right-angled triangle ABC, the leg AC = 55, and the height of the CH, lowered to the hypotenuse, is 44. Find the Sin of the angle ABC.

In a right-angled triangle ABC, the height of CH, lowered to the hypotenuse, forms a triangle AHC, which is also rectangular.

Right-angled triangles ABC and AHC are similar in one equal acute angle A.

Thus, the angle ACH of the triangle AHC is equal to the angle ABC of the triangle ABC.

So, in a right-angled triangle ACH AC = 55 is the hypotenuse, and CH = 44 is the leg adjacent to the ACH angle. According to the Pythagorean theorem, the opposite leg AH is equal to (55 ^ 2 – 44 ^ 2) ^ 0.5 = 33, then sin ACH = sin ABC = 33/55 = 0.6