To find the length of the other leg in a right triangle, you 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, one leg \(a = 6\) ft, and the hypotenuse \(c = 12\) ft. We need to find the length of the other leg \(b\).
Substituting the known values into the Pythagorean theorem:
\[ 6^2 + b^2 = 12^2 \]
Calculating \(6^2\) and \(12^2\):
\[ 36 + b^2 = 144 \]
Now, subtract \(36\) from both sides:
\[ b^2 = 144 - 36 \]
\[ b^2 = 108 \]
Next, take the square root of both sides to find \(b\):
\[ b = \sqrt{108} \]
Calculating \(\sqrt{108}\):
\[ b = \sqrt{36 \times 3} = 6\sqrt{3} \]
Now, approximate \(6\sqrt{3}\):
\[ \sqrt{3} \approx 1.732 \]
So,
\[ b \approx 6 \times 1.732 \approx 10.392 \]
Rounding to the nearest tenth:
\[ b \approx 10.4 \text{ ft} \]
Therefore, the length of the other leg is approximately 10.4 ft.