The two acute corners of a right-angled triangle are 3: 6. Find the largest of the corners.

Let’s denote by x the value of the smaller acute angle of this right-angled triangle.

According to the condition of the problem, the values ​​of the two acute angles of this right-angled triangle are related as 3: 6, which is 1: 2, therefore, one of the acute angles of this right-angled triangle is 2 times larger than the other, and the magnitude of the larger acute angle of this right-angled triangle is 2x.

Since the sum of all the angles of any triangle is 180 °, we can write the following equation:

90 + x + 2x = 180.

Solving this equation, we get:

90 + 3x = 180;

3x = 180 – 90;

3x = 90;

x = 90/3;

x = 30 °.

Find the second acute angle:

2x = 2 * 30 = 60 °.

Answer: the larger acute angle is 60 °.