In a right-angled triangle, the acute angles are proportional to the numbers 5:13. Find the difference between these angles.

Let x denote one-fifth of the smaller of the acute angles of this triangle.

Then this angle should be 5x degrees.

In the initial data for this task, it is reported that the ratio of the acute angles of this triangle is five to thirteen, therefore, the other of the acute angles of this triangle should be 13x degrees.

Since the sum of the values ​​of all 3 angles of a triangle is always 180 °, we can draw up the following equation:

13x + 5x + 90 = 180,

solving which, we get:

18x + 90 = 180;

18x = 180 – 90 = 90;

x = 90/18 = 5.

Find the difference between the acute angles:

13x – 5h = 8x = 8 * 5 = 40 °.

Answer: 40 °.