To find the length of the other leg of the right triangle, you can use the Pythagorean Theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( a \) and \( b \) are the legs of the triangle and \( c \) is the hypotenuse.
In this problem, we have:
- One leg \( a = 6 \) ft
- Hypotenuse \( c = 12 \) ft
- We need to find the other leg \( b \).
Substituting the known values into the equation:
\[ 6^2 + b^2 = 12^2 \] \[ 36 + b^2 = 144 \]
Now, subtract 36 from both sides:
\[ b^2 = 144 - 36 \] \[ b^2 = 108 \]
Next, take the square root of both sides to find \( b \):
\[ b = \sqrt{108} \] \[ b = \sqrt{36 \times 3} \] \[ b = 6\sqrt{3} \]
Now calculating \( 6\sqrt{3} \):
Using \( \sqrt{3} \approx 1.732 \):
\[ b \approx 6 \times 1.732 \] \[ b \approx 10.392 \]
Rounding to the nearest tenth:
The length of the other leg is approximately 10.4 ft.