To find the length of the other leg of a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs of the triangle.
Given:
- The hypotenuse (\(c\)) is 15 cm.
- One leg (\(a\)) is 9 cm.
- We need to find the other leg (\(b\)).
We can rearrange the formula to solve for \(b\):
\[ b^2 = c^2 - a^2 \]
Substituting in the known values:
\[ b^2 = 15^2 - 9^2 \]
Calculating the squares:
\[ b^2 = 225 - 81 \]
Now, subtract:
\[ b^2 = 144 \]
Next, take the square root of both sides to find \(b\):
\[ b = \sqrt{144} = 12 \]
Thus, the measure of the other leg is \( \boxed{12} \) cm.