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.
To find the length of the other leg in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given the length of one leg as 11 and the length of the hypotenuse as 22. Let's call the length of the other leg "x".
Using the Pythagorean theorem, we can write the equation:
11^2 + x^2 = 22^2
Simplifying the equation, we have:
121 + x^2 = 484
Now, subtract 121 from both sides of the equation:
x^2 = 363
To solve for x, we need to take the square root of both sides of the equation:
x = √363
Using a calculator, we find the approximate value of √363 is 19.052.
Rounding to two decimal places, the length of the other leg is approximately 19.05.
By the Pythagorean theorem, the length of the other leg can be found as:
√(22^2 - 11^2) = √(484 - 121) = √363 ≈ 19.06
The length of the other leg is approximately 19.06.