If a right triangle has a leg that is 6 ft. long and the hypotenuse is 12 ft. long, how long is the other leg? Round to the nearest tenth.(1 point)
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 is equal to the sum of the squares of the lengths of the two legs.
Let's denote the length of the other leg as "x". The given information tells us that one leg is 6 ft. long (denoted as "6") and the hypotenuse is 12 ft. long (denoted as "12").
Using the Pythagorean theorem:
x^2 + 6^2 = 12^2
Simplifying:
x^2 + 36 = 144
Subtracting 36 from both sides:
x^2 = 144 - 36
x^2 = 108
Now, we can take the square root of both sides to find x:
x = √108
Using a calculator, we find that √108 is approximately 10.39.
Rounding to the nearest tenth, the length of the other leg is 10.4 ft.
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 two legs.
In this case, we have one leg of 6 ft and a hypotenuse of 12 ft. Let's call the length of the other leg "x".
Using the Pythagorean theorem, we can set up the following equation:
x^2 + 6^2 = 12^2
Simplifying, we get:
x^2 + 36 = 144
Subtracting 36 from both sides, we have:
x^2 = 108
To find the length of x, we need to take the square root of both sides:
√(x^2) = √(108)
x = √(108)
Calculating the square root of 108, we find that x is approximately 10.39. Rounded to the nearest tenth, the length of the other leg is 10.4 ft.
Find the unknown side length in the given triangle. Round to the nearest hundredth. (1 point)
Description of image: Hypotenuse is 30, left leg is 20, and bottom leg is the unknown side length.
@BotGPT35
wrong
Its 10.4
Let the length of the other leg be x. According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be represented by the equation:
6^2 + x^2 = 12^2
Simplifying this equation, we have:
36 + x^2 = 144
Subtracting 36 from both sides, we get:
x^2 = 108
Taking the square root of both sides, we find:
x ≈ √108
x ≈ 10.39 ft
Therefore, the length of the other leg is approximately 10.39 ft.