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.

The height CD of a right-angled triangle ABC divides it into two right-angled triangles ACD and BCD.

In a right-angled triangle ACD tgCAD = CD / AD = 4/4 * √3 = 1 / √3.

Angle CAD = CAB = arctan (1 / √3) = 30.

Since the triangle ABC is rectangular, the angle ABC = (180 – 90 – CAD) = 90 – 30 = 60.

Answer: The degree measures of the acute angles of the triangle ABC are equal to 30 and 60.