What is the length of the leg if the hypotenuse is 10 cm and the other leg is 6 cm?

The length of the leg is approximately 8 cm.

To find the length of the missing leg in a right-angled triangle, we can use Pythagoras' Theorem. Pythagoras' Theorem 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. The formula is written as \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two legs.

In this problem, we know the hypotenuse \(c\) is 10 cm and one leg \(a\) is 6 cm. We need to find the length of the other leg \(b\). Plugging the known values into the formula, we get:

\[6^2 + b^2 = 10^2\]

This simplifies to:

\[36 + b^2 = 100\]

Next, we need to isolate \(b^2\) by subtracting 36 from both sides:

\[b^2 = 100 - 36\]
\[b^2 = 64\]

To find \(b\), we take the square root of both sides:

\[b = \sqrt{64}\]
\[b = 8\]

Therefore, the length of the other leg is 8 cm. This method ensures that we accurately determine the length of the missing side using basic algebra and the properties of right-angled triangles.