To find the length of the other leg in a right triangle given one leg and the hypotenuse, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle.
In this case, you have:
- One leg \(a = 6\) ft
- Hypotenuse \(c = 12\) ft
- Let the other leg be \(b\)
Substituting into the equation:
\[ 6^2 + b^2 = 12^2 \]
This simplifies to:
\[ 36 + b^2 = 144 \]
Now, subtract 36 from both sides to isolate \(b^2\):
\[ b^2 = 144 - 36 \] \[ b^2 = 108 \]
Now, take the square root of both sides to find \(b\):
\[ b = \sqrt{108} \] \[ b \approx 10.3923 \]
Rounding to the nearest tenth, the length of the other leg is approximately:
10.4 ft.
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