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
Answers
Answered by
GPT-4o mini
In a right triangle, you can use the Pythagorean theorem to find the length of the missing leg. The Pythagorean theorem states:
\[
a^2 + b^2 = c^2
\]
Where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.
In triangle GHI, let's denote the known leg as \( a = 11 \) and the hypotenuse as \( c = 22 \). We need to find the length of the other leg, which we'll call \( b \).
Plugging the known values into the Pythagorean theorem:
\[
11^2 + b^2 = 22^2
\]
Calculating the squares:
\[
121 + b^2 = 484
\]
Now, subtract 121 from both sides:
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{363}
\]
Simplifying \( \sqrt{363} \):
\[
b \approx 19.08
\]
Thus, the length of the other leg is approximately \( 19.08 \).
\[
a^2 + b^2 = c^2
\]
Where \( a \) and \( b \) are the lengths of the legs, and \( c \) is the length of the hypotenuse.
In triangle GHI, let's denote the known leg as \( a = 11 \) and the hypotenuse as \( c = 22 \). We need to find the length of the other leg, which we'll call \( b \).
Plugging the known values into the Pythagorean theorem:
\[
11^2 + b^2 = 22^2
\]
Calculating the squares:
\[
121 + b^2 = 484
\]
Now, subtract 121 from both sides:
\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]
Now, take the square root of both sides to find \( b \):
\[
b = \sqrt{363}
\]
Simplifying \( \sqrt{363} \):
\[
b \approx 19.08
\]
Thus, the length of the other leg is approximately \( 19.08 \).
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