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.(1 point)
wrong
By using the Pythagorean theorem, we know 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 two legs. Let the length of the unknown leg be x.
So, using the given information, we can write the equation:
11^2 + x^2 = 22^2
121 + x^2 = 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.
In a right triangle, the Pythagorean theorem can be used to find the length of the missing side.
The Pythagorean theorem states that in a 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 sides (a and b).
Mathematically, this can be expressed as:
c^2 = a^2 + b^2
Given that the length of one leg (a) is 11 and the hypotenuse (c) is 22, we can substitute these values into the equation:
(22)^2 = (11)^2 + b^2
484 = 121 + b^2
Subtracting 121 from both sides:
363 = b^2
Taking the square root of both sides:
b = sqrt(363)
Using a calculator, we can find the approximate value of sqrt(363) to be approximately 19.06.
Therefore, the length of the other leg (b) is approximately 19.06, rounded to two decimal places.
To find the length of the other leg of 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 (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's label the legs of the right triangle as a and b, and the hypotenuse as c. In this case, we are given that one leg (b) is 11 and the hypotenuse (c) is 22.
Using the Pythagorean theorem, we can write the equation: a^2 + b^2 = c^2.
Substituting the given values, we get: a^2 + 11^2 = 22^2.
Simplifying further: a^2 + 121 = 484.
To solve for a, we subtract 121 from both sides of the equation: a^2 = 363.
Next, we take the square root of both sides to find the length of the other leg, a: a = sqrt(363).
Evaluating the square root, we find that a is approximately 19.07.
Therefore, the length of the other leg of the right triangle is approximately 19.07, rounded to two decimal places.