How many feet long is the unknown side length of the right triangle?

A right triangle with one leg of length 5 feet and a hypotenuse of length 13 feet.

To find the length of the unknown side of the right triangle, we can use the Pythagorean theorem, which states that 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 the unknown side length be x.

So we have: 5^2 + x^2 = 13^2
25 + x^2 = 169
x^2 = 169 - 25
x^2 = 144
x = √144
x = 12

Therefore, the unknown side length of the right triangle is 12 feet.