Calculate Missing Leg of Right Triangle using Pythagorean Theorem

The image shows a right-angled triangle. The lengths of two sides are given: one leg is 60 cm, and the hypotenuse is 61 cm. We need to find the length of the other leg, labeled as .

We can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs). Mathematically, this is represented as:

where and are the lengths of the legs, and is the length of the hypotenuse.

In this problem, we have:

Substituting these values into the Pythagorean theorem:

Now, we need to solve for :
First, calculate the squares of 60 and 61:

Substitute these values back into the equation:

Now, isolate by subtracting 3600 from both sides of the equation:

To find , take the square root of both sides of the equation:

The square root of 121 is 11.

Therefore, the length of the other leg, , is 11 cm.

The final answer is .