If a right triangle has a leg that measures 8 inches and the hypotenuse is 12 inches, how long is the other leg? Round to the nearest tenth, if necessary.(1 point)
inches
To find the length of the other leg, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, one leg measures 8 inches and the hypotenuse is 12 inches. Let's call the other leg "x". So we have:
a = 8 inches
c = 12 inches
b = x inches
Using the Pythagorean theorem, we can write:
c^2 = a^2 + b^2
12^2 = 8^2 + x^2
144 = 64 + x^2
Next, let's subtract 64 from both sides of the equation:
144 - 64 = 64 + x^2 - 64
80 = x^2
To solve for x, we can take the square root of both sides of the equation:
√80 ≈ 8.94
So the length of the other leg is approximately 8.94 inches. Rounding to the nearest tenth, the other leg measures 8.9 inches.
To find the length of the other leg in a right triangle, we can use the Pythagorean Theorem. The theorem 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. According to the Pythagorean Theorem, we have:
x^2 + 8^2 = 12^2
Simplifying the equation, we get:
x^2 + 64 = 144
Subtracting 64 from both sides:
x^2 = 144 - 64
x^2 = 80
To find the value of x, we take the square root of both sides:
x = √80
x ≈ 8.9
Therefore, the length of the other leg of the right triangle is approximately 8.9 inches.
To find the length of the other leg in a right triangle, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, in this case, we have:
Hypotenuse^2 = Leg1^2 + Leg2^2
Given that the hypotenuse is 12 inches (Hypotenuse = 12), and one leg measures 8 inches (Leg1 = 8), we can substitute the values into the equation:
12^2 = 8^2 + Leg2^2
Simplifying this equation, we have:
144 = 64 + Leg2^2
Subtracting 64 from both sides, we get:
Leg2^2 = 80
To find the length of Leg2, we need to take the square root of both sides:
Leg2 = √80
Using a calculator or simplifying the square root, we find:
Leg2 ≈ 8.9 inches (rounded to the nearest tenth)
So, the length of the other leg is approximately 8.9 inches.