Pythagorean Theorem Proofs Practice

Complete this assessment to review what you've learned. It will not count toward your grade.
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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

1 answer

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:

\[ \boxed{19.08} \]

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