In a right-angled triangle, one of the acute angles is 60 degrees, and the leg adjacent to it is 12 cm. Find the lengths

In a right-angled triangle, one of the acute angles is 60 degrees, and the leg adjacent to it is 12 cm. Find the lengths of the segments by which the height drawn from the vertex of the right angle divides the hypotenuse.

Let in a right-angled triangle ABC, with a right angle C, legs a, b, hypotenuse c, height by the hypotenuse h by segments into which the hypotenuse is divided by height-BH -c (a), AH -c (b).
Let’s write the formulas:
h ^ 2 = c (a) * c (b), <A = 60, <B = 30. Cathetus b = c / 2, like a leg lying opposite an angle equal to 30 degrees in a right triangle.
Consider a triangle CHB: here a-hypotenuse, h-leg against an angle of 30 degrees.
h = a / 2 = 12/2 = 6.
Leg c (a) = (√3) / 2 * (12) = 6 * √ 3.
Then c (b) = h ^ 2 / c (a) = 6 ^ 2 / 6√3 = 2√3, c = c (a_ + c (b) = 8√3
And to check: a = [(√3) / 2] * c = [(√3) / 2] * 8√3 = 12. The solution is correct.