Question

If a right triangle has a leg that is 20ft long and the hypotenuse is 30ft long how long is the other leg? Round to the nearest hundredth

Answer 1

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**.