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 other two legs. In this case, we know one leg (let's call it \( a \)) is 11, and the hypotenuse \( c \) is 22.
Let \( b \) be the length of the other leg. Plugging in the values we have:
\[ 11^2 + b^2 = 22^2 \]
Calculating the squares:
\[ 121 + b^2 = 484 \]
Next, we subtract 121 from both sides to solve for \( b^2 \):
\[ b^2 = 484 - 121 \] \[ b^2 = 363 \]
Now, we take the square root of both sides to find \( b \):
\[ b = \sqrt{363} \]
Calculating \( \sqrt{363} \):
\[ b \approx 19.08 \]
Therefore, the length of the other leg rounded to two decimal places is approximately \( \boxed{19.08} \).