To find the length of the other leg of a right triangle given one leg and the hypotenuse, we can use the Pythagorean theorem. The theorem states:
\[ a^2 + b^2 = c^2 \]
where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse. In this case, we have one leg \(a = 12\) in. and hypotenuse \(c = 16\) in. We need to find the length of the other leg \(b\).
Plugging in the values we know:
\[ 12^2 + b^2 = 16^2 \]
Calculating the squares:
\[ 144 + b^2 = 256 \]
Now, we isolate \(b^2\):
\[ b^2 = 256 - 144 \] \[ b^2 = 112 \]
Next, we take the square root to find \(b\):
\[ b = \sqrt{112} \]
To simplify \(\sqrt{112}\):
\[ \sqrt{112} = \sqrt{16 \times 7} = 4\sqrt{7} \]
To find an approximate value, we can calculate \(\sqrt{7}\) (which is about 2.64575):
\[ b \approx 4 \times 2.64575 \approx 10.583 \]
Thus, the length of the other leg is approximately 10.6 inches.