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.

Answer 1

19.05

Answer 2

To find the length of the other leg in the right triangle GHI, we can use the Pythagorean theorem. The theorem states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \):

\[
a^2 + b^2 = c^2
\]

In this case, we know one leg \( a = 11 \) and the hypotenuse \( c = 22 \). We need to find the length of the other leg \( b \).

First, we substitute the known values into the Pythagorean theorem:

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

Calculating each square:

\[
121 + b^2 = 484
\]

Next, we isolate \( b^2 \):

\[
b^2 = 484 - 121
\]

Calculating the right-hand side:

\[
b^2 = 363
\]

Now, we find \( b \) by taking the square root of both sides:

\[
b = \sqrt{363}
\]

Using a calculator to compute \( \sqrt{363} \):

\[
b \approx 19.1
\]

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

\[
\boxed{19.10}
\]