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)
19.05
1. 2
2. 4
3. 9^2+12^2=c^2
4. 20
5. 19.05
19.07 is not the answer
If the answer isn't 19.06 nor 19.07, what's the real answer?
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... Your Answers are correct congrats! you should get 100!
To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which 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 legs.
Let's denote the length of the other leg as x. We know that one leg is 11 and the hypotenuse is 22.
Using the Pythagorean theorem, we can write:
11^2 + x^2 = 22^2
Simplifying this equation, we have:
121 + x^2 = 484
Subtracting 121 from both sides, we get:
x^2 = 363
Taking the square root of both sides, we find:
x = √363
Rounding this answer to two decimal places, the length of the other leg (GH) is approximately 19.06.
Since we know that triangle GHI is a right triangle and one leg is 11 while the hypotenuse is 22, we can use the Pythagorean theorem to find the length of the other leg.
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, it can be written as:
c^2 = a^2 + b^2
We are given that the hypotenuse (c) is 22 and one leg (a) is 11. We need to find the length of the other leg (b).
Plugging in the given values into the Pythagorean theorem equation, we have:
22^2 = 11^2 + b^2
Simplifying, we have:
484 = 121 + b^2
Subtracting 121 from both sides, we get:
363 = b^2
To find b, we need to take the square root of both sides:
b = √363
Using a calculator, we can find the square root of 363:
b ≈ 19.07
Therefore, the length of the other leg is approximately 19.07 (rounded to two decimal places).
Using the Pythagorean theorem, the length of the other leg can be found by:
other leg = √(hypotenuse^2 - leg^2)
other leg = √(22^2 - 11^2)
other leg = √(484 - 121)
other leg = √363
other leg ≈ 19.07
So, the length of the other leg is approximately 19.07.