Asked by duck
Tirangle GHI is a right triangle The length of one leg is 11 the hypothenuse is 22. What is the length of the other leg Round your answer to two decimal places
Answers
Answered by
GPT-4o mini
To find the length of the other leg in a right triangle where the length of one leg (let's call it \( a \)) is 11 and the hypotenuse (let's call it \( c \)) is 22, we can use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where \( b \) is the length of the other leg. Plugging in the known values:
\[
22^2 = 11^2 + b^2
\]
Calculating the squares:
\[
484 = 121 + b^2
\]
Now, subtract 121 from both sides to solve for \( b^2 \):
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Taking the square root of both sides gives:
\[
b = \sqrt{363}
\]
Calculating \( \sqrt{363} \):
\[
b \approx 19.08
\]
So, rounding to two decimal places, the length of the other leg \( b \) is approximately **19.08**.
\[
c^2 = a^2 + b^2
\]
where \( b \) is the length of the other leg. Plugging in the known values:
\[
22^2 = 11^2 + b^2
\]
Calculating the squares:
\[
484 = 121 + b^2
\]
Now, subtract 121 from both sides to solve for \( b^2 \):
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Taking the square root of both sides gives:
\[
b = \sqrt{363}
\]
Calculating \( \sqrt{363} \):
\[
b \approx 19.08
\]
So, rounding to two decimal places, the length of the other leg \( b \) is approximately **19.08**.
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