To find the length of the other leg in a right triangle where the length of one leg (let's call it \( a \)) is 11 and the hypotenuse (let's call it \( c \)) is 22, we can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \( b \) is the length of the other leg. Plugging in the known values:
\[ 22^2 = 11^2 + b^2 \]
Calculating the squares:
\[ 484 = 121 + b^2 \]
Now, subtract 121 from both sides to solve for \( b^2 \):
\[ b^2 = 484 - 121 \] \[ b^2 = 363 \]
Taking the square root of both sides gives:
\[ b = \sqrt{363} \]
Calculating \( \sqrt{363} \):
\[ b \approx 19.08 \]
So, rounding to two decimal places, the length of the other leg \( b \) is approximately 19.08.
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