To find the length of the other leg of a right triangle using the Pythagorean Theorem, you can use the formula:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, you know one leg (\( a = 6 \) ft) and the hypotenuse (\( c = 12 \) ft). You need to find the other leg (\( b \)).
Plugging in the values:
\[ 6^2 + b^2 = 12^2 \]
Calculating the squares:
\[ 36 + b^2 = 144 \]
Now subtract 36 from both sides:
\[ b^2 = 144 - 36 \]
\[ b^2 = 108 \]
Next, take the square root of both sides to find \( b \):
\[ b = \sqrt{108} \]
To simplify \( \sqrt{108} \):
\[ \sqrt{108} = \sqrt{36 \cdot 3} = 6\sqrt{3} \]
Now, calculating \( 6\sqrt{3} \) gives approximately:
\[ 6 \times 1.732 \approx 10.392 \]
Rounding to the nearest tenth:
The length of the other leg is approximately 10.4 ft.