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
no none of the answers are right
In a right triangle, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let the length of the other leg be denoted by x.
Thus, using the Pythagorean theorem, we can write:
x^2 + 11^2 = 22^2
x^2 + 121 = 484
x^2 = 484 - 121
x^2 = 363
Taking the square root of both sides, we get:
x = √363
x ≈ 19.06
Therefore, the length of the other leg is approximately 19.06 units.
To find the length of the other leg (abbreviated as "l"), you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (h) is equal to the sum of the squares of the other two sides.
The formula is: h^2 = l^2 + w^2
Given that the hypotenuse (h) is 22 and one leg (w) is 11, we can substitute these values into the formula and solve for the length of the other leg (l).
22^2 = l^2 + 11^2
Simplifying:
484 = l^2 + 121
Rearranging the equation:
l^2 = 484 - 121
l^2 = 363
To find the value of l, take the square root of both sides:
l = √363
Using a calculator, we find that the value of l is approximately 19.07 when rounded to two decimal places.
Therefore, the length of the other leg (GH) is approximately 19.07 units.
To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two legs.
In this case, the square of the hypotenuse is 22^2 = 484, and the square of one leg is 11^2 = 121.
Let's denote the length of the other leg as x.
Using the Pythagorean theorem: hypotenuse^2 = leg1^2 + leg2^2
Substituting the known values: 484 = 121 + x^2
Rearranging the equation: x^2 = 484 - 121
Simplifying: x^2 = 363
To find the length of the other leg, we need to take the square root of both sides of the equation:
sqrt(x^2) = sqrt(363)
x = sqrt(363)
Calculating the square root of 363, we find that the length of the other leg is approximately 19.07 (rounded to two decimal places).
Therefore, the length of the other leg in triangle GHI is approximately 19.07.