To find the length of the other leg of a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Here, \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, we know one leg (\(a = 15\)) and the hypotenuse (\(c = 22\)). We need to find the length of the other leg (\(b\)).
First, we can plug the known values into the equation:
\[ 15^2 + b^2 = 22^2 \]
Calculating the squares:
\[ 225 + b^2 = 484 \]
Now, we subtract 225 from both sides to isolate \(b^2\):
\[ b^2 = 484 - 225 \]
Calculating the right side:
\[ b^2 = 259 \]
Next, we take the square root of both sides to find \(b\):
\[ b = \sqrt{259} \]
Calculating \(\sqrt{259}\):
\[ b \approx 16.1 \]
Thus, the length of the other leg, rounded to the nearest tenth, is:
\[ \boxed{16.1} \]
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