In a right triangle, we can use the Pythagorean theorem to find the length of the unknown leg. The Pythagorean theorem states that:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the lengths of the legs and \( c \) is the length of the hypotenuse.
In this case, we know one leg \( a = 11 \) and the hypotenuse \( c = 22 \). We need to find the length of the other leg \( b \). Plugging in the values we have:
\[ 11^2 + b^2 = 22^2 \]
Calculating the squares:
\[ 121 + b^2 = 484 \]
Now, we can isolate \( b^2 \):
\[ b^2 = 484 - 121 \] \[ b^2 = 363 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{363} \approx 19.08 \]
Therefore, the length of the other leg is approximately \( 19.08 \) when rounded to two decimal places.