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.
Let's call the other leg "x". According to the Pythagorean theorem, the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
So, 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 = 256 - 144
x^2 = 112
Taking the square root of both sides, we find:
x = √112
Simplifying the square root, we have:
x ≈ 10.6
Therefore, the length of the other leg is approximately 10.6.