To find the length of the other leg in a right triangle where one leg is 12 and the hypotenuse is 16, we can use the Pythagorean theorem, which states that:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.
In this case, let \( a = 12 \), \( c = 16 \), and \( b \) be the unknown leg. We can rearrange the formula to solve for \( b \):
\[ b^2 = c^2 - a^2 \]
Now, plugging in the values:
\[ b^2 = 16^2 - 12^2 \] \[ b^2 = 256 - 144 \] \[ b^2 = 112 \]
Now, taking the square root of both sides to find \( b \):
\[ b = \sqrt{112} \]
To simplify \( \sqrt{112} \):
\[ \sqrt{112} = \sqrt{16 \times 7} = 4\sqrt{7} \]
Now, calculating \( 4\sqrt{7} \):
Using a calculator, \( \sqrt{7} \approx 2.6458 \).
Thus,
\[ b \approx 4 \times 2.6458 \approx 10.5832 \]
Rounding to the nearest tenth:
\[ b \approx 10.6 \]
Therefore, the length of the other leg is approximately \( 10.6 \).