If a right triangle has a leg that is 6 feet long and the hypotenuse is 12 feet long, how long is the other leg?
Let's call the other leg of the right triangle "x".
According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs.
In this case, we have:
12² = 6² + x²
144 = 36 + x²
Now, subtract 36 from both sides of the equation:
144 - 36 = x²
108 = x²
To find the length of the other leg, we take the square root of both sides:
√108 = √x²
10.39 ≈ x
Therefore, the length of the other leg is approximately 10.39 feet.
To find the length of the other leg, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Let's denote the length of the other leg as 'x'. We have the following equation:
x^2 + 6^2 = 12^2
Simplifying the equation, we get:
x^2 + 36 = 144
Subtracting 36 from both sides:
x^2 = 108
Now, taking the square root of both sides:
x = √108
Simplifying the square root, we get:
x ≈ 10.39
Therefore, the length of the other leg is approximately 10.39 feet.
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 other two sides.
In this case, we can represent the lengths of the legs and the hypotenuse as follows:
Length of one leg = 6 feet
Length of the other leg = x (unknown)
Length of the hypotenuse = 12 feet
According to the Pythagorean theorem, we can write the equation:
(Length of one leg)^2 + (Length of the other leg)^2 = (Length of the hypotenuse)^2
Substituting the given lengths into the equation, we have:
6^2 + x^2 = 12^2
Simplifying the equation, we get:
36 + x^2 = 144
To isolate x^2, we subtract 36 from both sides:
x^2 = 144 - 36
x^2 = 108
To solve for x, we take the square root of both sides:
x = √108
Simplifying the square root, we get:
x ≈ 10.3923048454
Therefore, the length of the other leg of the right triangle is approximately 10.39 feet.