To find the length of the other leg in a right triangle using the Pythagorean theorem, we can use the formula:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) and \(b\) are the lengths of the legs,
- \(c\) is the length of the hypotenuse.
In this case, we have:
- One leg \(a = 11\),
- Hypotenuse \(c = 22\),
- The other leg is \(b\).
Substituting the known values into the Pythagorean theorem:
\[ 11^2 + b^2 = 22^2 \]
Calculating \(11^2\) and \(22^2\):
\[ 121 + b^2 = 484 \]
Now, we can isolate \(b^2\):
\[ b^2 = 484 - 121 \]
Calculating \(484 - 121\):
\[ b^2 = 363 \]
Now, to find the length of leg \(b\), we take the square root of both sides:
\[ b = \sqrt{363} \approx 19.08 \]
Therefore, rounding to two decimal places, the length of the other leg is:
\[ \boxed{19.08} \]
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