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

1 answer

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 \( \boxed{19.08} \).