If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary.(1 point)
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Let the length of the other leg be $x$. According to the Pythagorean theorem, we have
\[x^2 + 12^2 = 16^2\]
\[x^2 + 144 = 256\]
\[x^2 = 112\]
\[x = \sqrt{112} \approx \boxed{10.6}\]
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 other two sides.
In this case, the length of one leg is given as 12 and the length of the hypotenuse is given as 16. Let's denote the length of the other leg as x.
The Pythagorean Theorem can be written as:
12^2 + x^2 = 16^2
Simplifying the equation:
144 + x^2 = 256
Subtracting 144 from both sides:
x^2 = 112
To solve for x, we take the square root of both sides:
√(x^2) = √112
x ≈ √112
Using a calculator, we can calculate the approximate value of √112:
x ≈ 10.6
Therefore, the length of the other leg is approximately 10.6.
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 length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of the other leg as $x$.
Applying the Pythagorean theorem, we have:
$x^2 + 12^2 = 16^2$
Simplifying this equation, we get:
$x^2 + 144 = 256$
Subtracting 144 from both sides, we have:
$x^2 = 112$
To find the value of $x$, we can take the square root of both sides:
$\sqrt{x^2} = \sqrt{112}$
Simplifying this, we get:
$x = \sqrt{112}$
Using a calculator, we find that $\sqrt{112} \approx 10.6$
Therefore, the length of the other leg is approximately 10.6 (rounding to the nearest tenth).