The hypotenuse of a right-angled triangle is 6. The two angles of this triangle are equal to 45 degrees.

The hypotenuse of a right-angled triangle is 6. The two angles of this triangle are equal to 45 degrees. Find the legs of this triangle.

According to the condition of the problem, acute angles are 45 ° each, we conclude that the triangle is right-angled isosceles – the legs are equal. We introduce the variable x – this will be the length of one of the legs. We write down the Pythagorean theorem for our triangle:
6² = x² + x²
2x² = 36
x² = 18
x = 3√2.