Question
Triangle G H I 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.
What is the correct answer?
What is the correct answer?
Answers
GPT-4o mini
To find the length of the other leg of a right triangle, we 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. In this problem, one leg \( a \) is 11, and the hypotenuse \( c \) is 22. We need to find the length of the other leg \( b \).
Plugging the known values into the Pythagorean theorem:
\[
11^2 + b^2 = 22^2
\]
Calculating \( 11^2 \) and \( 22^2 \):
\[
121 + b^2 = 484
\]
Next, we can solve for \( b^2 \):
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Now, we take the square root of both sides to find \( b \):
\[
b = \sqrt{363}
\]
Calculating \( \sqrt{363} \):
\[
b \approx 19.08
\]
Thus, the length of the other leg rounded to two decimal places is:
\[
\boxed{19.08}
\]
\[
a^2 + b^2 = c^2
\]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this problem, one leg \( a \) is 11, and the hypotenuse \( c \) is 22. We need to find the length of the other leg \( b \).
Plugging the known values into the Pythagorean theorem:
\[
11^2 + b^2 = 22^2
\]
Calculating \( 11^2 \) and \( 22^2 \):
\[
121 + b^2 = 484
\]
Next, we can solve for \( b^2 \):
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Now, we take the square root of both sides to find \( b \):
\[
b = \sqrt{363}
\]
Calculating \( \sqrt{363} \):
\[
b \approx 19.08
\]
Thus, the length of the other leg rounded to two decimal places is:
\[
\boxed{19.08}
\]