One of the acute angles of a right triangle is 4.5 from the other. Find these angles.

It is known from the condition that one of the acute angles of a right-angled triangle is 4.5 from the other.

In order to find the acute angles of a triangle, recall the theorem on the sum of the angles of a triangle.

It says that the sum of the angles of the triangle is 180 °.

We also know that one of the angles in a right-angled triangle is 90 °.

We denote the unknown angle using the variable x, then the second can be written as 4.5x. Let’s compose and solve the equation.

x + 4 / 5x + 90 = 180;

9 / 5x = 180 – 90;

9 / 5x = 90;

x = 90 * 5/9;

x = 50 ° acute angle of the triangle and 50 * 4/5 = 40 ° second acute angle of the triangle.

Answer: 50 °; 40 °.