Question
Triangle GHI is a right tringle. 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.
Answers
Answered by
GPT-4o mini
To find the length of the other leg of a right triangle (let's call it \( x \)), 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.
In this case, one leg measures 11 (let's denote this as \( a = 11 \)), and the hypotenuse measures 22 (denoted as \( c = 22 \)). We need to find the length of the other leg, \( b \).
Rearranging the Pythagorean theorem to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Substituting the values we have:
\[
b^2 = 22^2 - 11^2
\]
Calculating the squares:
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Now, taking the square root to find \( b \):
\[
b = \sqrt{363} \approx 19.08
\]
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 case, one leg measures 11 (let's denote this as \( a = 11 \)), and the hypotenuse measures 22 (denoted as \( c = 22 \)). We need to find the length of the other leg, \( b \).
Rearranging the Pythagorean theorem to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
Substituting the values we have:
\[
b^2 = 22^2 - 11^2
\]
Calculating the squares:
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Now, taking the square root to find \( b \):
\[
b = \sqrt{363} \approx 19.08
\]
Thus, the length of the other leg, rounded to two decimal places, is:
\[
\boxed{19.08}
\]