To find the length of the other leg of a right triangle when one leg and the hypotenuse are known, 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 legs.
In this case, let’s let \( a = 12 \) in (one leg) and \( c = 16 \) in (the hypotenuse). We want to find \( b \) (the other leg).
Plugging the known values into the equation:
\[ 12^2 + b^2 = 16^2 \]
Calculating the squares:
\[ 144 + b^2 = 256 \]
Now, subtract 144 from both sides:
\[ b^2 = 256 - 144 \] \[ b^2 = 112 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{112} \]
Calculating the square root:
\[ b \approx 10.583 \]
Rounding to one decimal place gives \( b \approx 10.6 \).
So the approximate length of the other leg is \( \boxed{10.6} \) inches.