To find the length of the other leg in a right triangle, we 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 the given triangle:
- One leg (let's call it \( a \)) is 6 ft.
- The hypotenuse (let's call it \( c \)) is 12 ft.
- We need to find the length of the other leg (let's call it \( b \)).
Using the Pythagorean theorem:
\[ 6^2 + b^2 = 12^2 \]
Calculating the squares:
\[ 36 + b^2 = 144 \]
Now, subtract 36 from both sides:
\[ b^2 = 144 - 36 \] \[ b^2 = 108 \]
Now take the square root of both sides to find \( b \):
\[ b = \sqrt{108} \]
To simplify \( \sqrt{108} \):
\[ \sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3} \]
Now, we can calculate \( 6\sqrt{3} \). The approximate value of \( \sqrt{3} \) is about 1.732.
So:
\[ b \approx 6 \times 1.732 \approx 10.392 \]
Rounding to the nearest tenth:
\[ b \approx 10.4 \text{ ft} \]
Thus, the length of the other leg is approximately 10.4 ft.
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