To find the length of the missing leg in a right triangle where one leg is 12 feet and the hypotenuse is 20 feet, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
Here, \(c\) is the length of the hypotenuse (20 feet), \(a\) is one leg (12 feet), and \(b\) is the missing leg.
Plugging in the known values:
\[ 12^2 + b^2 = 20^2 \]
Calculating the squares:
\[ 144 + b^2 = 400 \]
Now, subtract 144 from both sides:
\[ b^2 = 400 - 144 \]
\[ b^2 = 256 \]
Now take the square root of both sides to find \(b\):
\[ b = \sqrt{256} \]
\[ b = 16 \]
Thus, the length of the missing leg \(b\) is \(16\) feet.
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