Triangle G H I is a right triangle. The length of one leg is 11 and the hypotenuse is 22. What is the length of the other leg? around your answer to two decimal places.
In a right triangle, using the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs.
Let the length of the other leg be x.
According to the given information, the hypotenuse is 22 and one leg is 11.
Therefore, we can write the equation as follows:
x^2 + 11^2 = 22^2
This simplifies to:
x^2 + 121 = 484
Now, subtract 121 from both sides of the equation:
x^2 = 363
To find the value of x, take the square root of both sides of the equation:
x = √363
Using a calculator, you'll find that the square root of 363 is approximately 19.07.
Therefore, the length of the other leg, rounded to two decimal places, is approximately 19.07.
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 sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Let's denote the length of the other leg as x. According to the theorem, we have:
x^2 + 11^2 = 22^2
Simplifying the equation:
x^2 + 121 = 484
Subtracting 121 from both sides:
x^2 = 363
Now, let's find the square root of both sides to solve for x:
x = √363
Using a calculator, we find:
x ≈ 19.07
Therefore, the length of the other leg is approximately 19.07 units (rounded to two decimal places).
To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in any right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
Let's label the length of the missing leg as x. According to the Pythagorean theorem, we have the equation:
11^2 + x^2 = 22^2
Simplifying this:
121 + x^2 = 484
Now, we can solve for x by isolating x^2:
x^2 = 484 - 121
x^2 = 363
Taking the square root of both sides:
x = √363
Now, to find the length of the other leg rounded to two decimal places, we can evaluate √363 using a calculator or online math tool:
x ≈ 19.07
Therefore, the length of the other leg is approximately 19.07.