One acute angle of a right triangle is 11 more than the other, find the larger acute angle.

From the condition, we know that one acute angle of a right-angled triangle is 11 ° larger than the other.

In order to find the larger acute angle of a triangle, let’s recall the theorem on the sum of the angles of a triangle.

The angles of a triangle add up to 180 °.

In a right-angled triangle, one angle is 90 °, the second angle is denoted by the variable x, and the third is written as (x + 11).

Let’s compose and solve the equation:

x + x + 11 + 90 = 180;

2x = 180 – 90 – 11;

2x = 79;

x = 79: 2;

x = 39.5 °;

One of the acute angles is 39.5 °; and the second 39.5 ° + 11 = 50.5 °