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.
We can use the Pythagorean theorem to find the length of the other leg. 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. Let's denote the length of the other leg as $x$.
Using the Pythagorean theorem, we have:
$x^2 + 12^2 = 16^2$
Simplifying, we have:
$x^2 + 144 = 256$
Subtracting 144 from both sides, we get:
$x^2 = 112$
Taking the square root of both sides, we have:
$x \approx \sqrt{112}$
Approximating the square root of 112 to the nearest tenth, we have:
$x \approx 10.6$
Therefore, the length of the other leg is approximately 10.6 units.