To find the length of the other leg of a right triangle when one leg and the hypotenuse are known, you 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. Given:
- One leg (\(a\)) = 20 ft
- Hypotenuse (\(c\)) = 30 ft
We need to find the other leg (\(b\)). Rearranging the Pythagorean theorem gives us:
\[ b^2 = c^2 - a^2 \]
Now, substitute the known values:
\[ b^2 = 30^2 - 20^2 \] \[ b^2 = 900 - 400 \] \[ b^2 = 500 \]
Now take the square root of both sides to find \(b\):
\[ b = \sqrt{500} \approx 22.36 \text{ ft} \]
Thus, the length of the other leg, rounded to the nearest hundredth, is approximately 22.36 ft.