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 answer

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.