The height CD of right-angled triangle ABC, drawn from the vertex of the right angle, is 4 cm.

The height CD of right-angled triangle ABC, drawn from the vertex of the right angle, is 4 cm. It is known that it divides the hypotenuse into segments, one of which is 4√3 cm. Find the degree measures of acute angles of triangle ABC.

Let AD = 4 * root (3).
The CDA triangle is rectangular, so tg (CAD) = CD / DA = 4 / (4 * root (3)) = 1 / root (3)
CAD = 30 degrees.
Angles of triangle ABC:
CAB + ABC + BCA = 180
30 + ABC + 90 = 180
ABC = 180 – 30 – 90 = 60
Answer: 30 degrees and 60 degrees.