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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.