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)
ft.
To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which 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 two legs (a and b).
In this case, we are given that one leg (a) is 6 ft and the hypotenuse (c) is 12 ft.
Using the Pythagorean theorem, we can write the formula as:
a^2 + b^2 = c^2
Solving for b:
b^2 = c^2 - a^2
b^2 = 12^2 - 6^2
b^2 = 144 - 36
b^2 = 108
To find the length of the other leg (b), we take the square root of 108:
b = √108
Using a calculator, we find that the square root of 108 is approximately 10.4.
Therefore, the length of the other leg of the right triangle is approximately 10.4 ft.
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 hypotenuse is equal to the sum of the squares of the other two sides.
Let's call the length of the other leg x.
Using the Pythagorean theorem, we can set up the equation:
x^2 + 6^2 = 12^2
Simplifying, we have:
x^2 + 36 = 144
Subtracting 36 from both sides:
x^2 = 108
Taking the square root of both sides to solve for x:
√(x^2) = √108
x = 10.4
Therefore, the length of the other leg of the right triangle is approximately 10.4 ft.
To solve this problem, 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 lengths of the legs as 'a' and 'b', and the length of the hypotenuse as 'c'.
According to the problem, we know that one leg is 6 ft. long (let's call it 'a') and the hypotenuse is 12 ft. long (let's call it 'c'). We are asked to find the length of the other leg (let's call it 'b').
Using the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = c^2
Substituting the values we have:
6^2 + b^2 = 12^2
36 + b^2 = 144
Now, let's solve for 'b':
b^2 = 144 - 36
b^2 = 108
Taking the square root of both sides:
b = √(108)
Calculating this:
b ≈ 10.39 ft.
Therefore, the length of the other leg, rounded to the nearest tenth, is approximately 10.39 ft.