In a right-angled triangle, the hypotenuse = √13, leg = 3. find the leg of the triangle

Consider a right-angled triangle. According to the Pythagorean theorem in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Let the unknown leg be equal to x. Since, according to the condition of the problem, the second leg is 3, and the hypotenuse is equal to √13, we compose a quadratic equation and find its roots:

x² + 3² = (√13) ²;

x² + 9 = 13;

x² = 13 – 9;

x² = 4;

x = 2.

We got the root of the quadratic equation x = 2, since through x we denoted the length of the second leg, the answer: the second leg is 2.