Tirangle GHI is a right triangle The length of one leg is 11 the hypothenuse is 22. What is the length of the other leg Round your answer to two decimal places

1 answer

To find the length of the other leg in a right triangle where the length of one leg (let's call it \( a \)) is 11 and the hypotenuse (let's call it \( c \)) is 22, we can use the Pythagorean theorem, which states:

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

where \( b \) is the length of the other leg. Plugging in the known values:

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

Calculating the squares:

\[ 484 = 121 + b^2 \]

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

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

Taking the square root of both sides gives:

\[ b = \sqrt{363} \]

Calculating \( \sqrt{363} \):

\[ b \approx 19.08 \]

So, rounding to two decimal places, the length of the other leg \( b \) is approximately 19.08.