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 to two decimal places

Answer 1

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 other two legs. In this case, we know one leg (let's call it \( a \)) is 11, and the hypotenuse \( c \) is 22.

Let \( b \) be the length of the other leg. Plugging in the values we have:

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

Calculating the squares:

\[
121 + b^2 = 484
\]

Next, we subtract 121 from both sides to 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 \( \sqrt{363} \):

\[
b \approx 19.08
\]

Therefore, the length of the other leg rounded to two decimal places is approximately \( \boxed{19.08} \).