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 ather leg? Round your answer to two decimal places. (1 point)

Answer 1

To find the length of the other leg of triangle GHI, we can use the Pythagorean theorem. The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two legs (a and b). This can be expressed with the formula:

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

In this case, we know that:
- One leg (a) = 11
- Hypotenuse (c) = 22
- Let the unknown leg be (b).

Substituting the known values into the Pythagorean theorem gives:

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

Calculating the squares:

\[
484 = 121 + b^2
\]

Now, subtract 121 from both sides to solve for \( b^2 \):

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

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

\[
b = \sqrt{363} \approx 19.08
\]

Therefore, rounding to two decimal places, the length of the other leg is:

\[
\boxed{19.08}
\]