To find the length of the other leg in a right triangle where one leg is 12 inches and the hypotenuse is 16 inches, we can use the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. Here, we have:
- One leg \( a = 12 \) inches
- Hypotenuse \( c = 16 \) inches
We need to find the other leg \( b \). Plugging in the values we have:
\[ 12^2 + b^2 = 16^2 \]
Calculating the squares:
\[ 144 + b^2 = 256 \]
Subtracting 144 from both sides:
\[ b^2 = 256 - 144 \] \[ b^2 = 112 \]
Now, taking the square root of both sides to find \( b \):
\[ b = \sqrt{112} \]
We can simplify \( \sqrt{112} \):
\[ \sqrt{112} = \sqrt{16 \times 7} = \sqrt{16} \times \sqrt{7} = 4\sqrt{7} \]
Using a calculator for an approximate value of \( \sqrt{7} \approx 2.64575 \):
\[ b \approx 4 \times 2.64575 \approx 10.583 \]
Thus, the length of the other leg is approximately \( 10.58 \) inches.
Therefore, the other leg must be approximately 10.58 inches.