To find the length of the other leg in 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. We know one leg, which we'll take as \(a = 11\), and the hypotenuse \(c = 22\).
We need to find the other leg \(b\). Plugging in the known values:
\[ 11^2 + b^2 = 22^2 \]
Calculating the squares:
\[ 121 + b^2 = 484 \]
Now, we can solve for \(b^2\):
\[ b^2 = 484 - 121 \] \[ b^2 = 363 \]
Taking the square root of both sides to find \(b\):
\[ b = \sqrt{363} \]
Calculating the square root:
\[ b \approx 19.08 \]
Rounding to two decimal places, the length of the other leg is:
\[ \boxed{19.08} \]