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.
Using the Pythagorean theorem, the length of the other leg can be found.
Let the length of the other leg be x.
By the Pythagorean theorem, we have:
x^2 + 6^2 = 12^2
Simplifying the equation:
x^2 + 36 = 144
Subtracting 36 from both sides:
x^2 = 144 - 36
x^2 = 108
Taking the square root of both sides:
x = √108 ≈ 10.4
Therefore, the length of the other leg is approximately 10.4 ft (rounded to the nearest tenth).
To find the length of the other leg of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
Let's label the unknown leg as 'a'. The given leg is 'b' and the hypotenuse is 'c'.
We have b = 6 ft and c = 12 ft.
According to the Pythagorean theorem:
a^2 + b^2 = c^2
Substituting the given values:
a^2 + (6 ft)^2 = (12 ft)^2
a^2 + 36 ft^2 = 144 ft^2
Now, let's solve for 'a':
a^2 = 144 ft^2 - 36 ft^2
a^2 = 108 ft^2
Taking the square root of both sides:
a ≈ √108 ft
a ≈ 10.4 ft (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 10.4 ft.
To determine the length of the other leg in a right triangle, you can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs.
In this case, we have the following information:
One leg = 6 ft
Hypotenuse = 12 ft
Let's call the other leg "x." We can set up the equation using the Pythagorean theorem:
x^2 + 6^2 = 12^2
Simplifying, we have:
x^2 + 36 = 144
Subtracting 36 from both sides:
x^2 = 108
To find x, we take the square root of both sides:
√(x^2) = √108
x ≈ 10.3923
Therefore, the length of the other leg, rounded to the nearest tenth, is approximately 10.4 ft.