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 point)

Answer 1

To find the length of the other leg of the right triangle GHI, 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 case:

- Let \( a = 11 \) (one leg)
- Let \( b \) be the unknown leg length
- Let \( c = 22 \) (the hypotenuse)

Substituting the values into the equation gives us:

\[
11^2 + b^2 = 22^2
\]

Calculating the squares:

\[
121 + b^2 = 484
\]

Now, subtract 121 from both sides:

\[
b^2 = 484 - 121
\]
\[
b^2 = 363
\]

Next, take the square root of both sides to find \( b \):

\[
b = \sqrt{363}
\]

Calculating the square root:

\[
b \approx 19.08
\]

Thus, the length of the other leg rounded to two decimal places is:

\[
\boxed{19.08}
\]