Question

Pythagorean Theorem Proofs Practice
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Question
Triangle GHI
is a right triangle. The length of one leg is 11 and the hypotenuse is 22. What is the length of the other leg? Round your answer to two decimal places

Answer 1

To find the length of the other leg in a right triangle using the Pythagorean theorem, we can use the formula:

\[
a^2 + b^2 = c^2
\]

where:
- \(a\) and \(b\) are the lengths of the legs,
- \(c\) is the length of the hypotenuse.

In this case, we have:
- One leg \(a = 11\),
- Hypotenuse \(c = 22\),
- The other leg is \(b\).

Substituting the known values into the Pythagorean theorem:

\[
11^2 + b^2 = 22^2
\]

Calculating \(11^2\) and \(22^2\):

\[
121 + b^2 = 484
\]

Now, we can isolate \(b^2\):

\[
b^2 = 484 - 121
\]

Calculating \(484 - 121\):

\[
b^2 = 363
\]

Now, to find the length of leg \(b\), we take the square root of both sides:

\[
b = \sqrt{363} \approx 19.08
\]

Therefore, rounding to two decimal places, the length of the other leg is:

\[
\boxed{19.08}
\]