To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, we know one leg \( a = 12 \) and the hypotenuse \( c = 16 \).
Substituting the known values into the equation:
\[ 12^2 + b^2 = 16^2 \]
Calculating the squares:
\[ 144 + b^2 = 256 \]
Next, subtract 144 from both sides:
\[ b^2 = 256 - 144 \] \[ b^2 = 112 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{112} \]
To simplify \( \sqrt{112} \):
\[ \sqrt{112} = \sqrt{16 \times 7} = \sqrt{16} \times \sqrt{7} = 4\sqrt{7} \]
Calculating \( \sqrt{7} \) (approximately 2.64575):
\[ b \approx 4 \times 2.64575 \approx 10.583 \]
Rounding to the nearest tenth:
\[ b \approx 10.6 \]
Thus, the length of the other leg is approximately 10.6.