We have a right triangle as indicated by the square angle marker. Two of the sides are known: specifically the hypotenuse (13) and one of the legs (12). The other leg (x) is unknown.
We can use the Pythagorean Theorem to find x
a = 12 is one of the known legs b = x is the unknown leg c = 13 is the hypotenuse
Pythagorean Theorem: a^2 + b^2 = c^2 12^2 + x^2 = 13^2 144 + x^2 = 169 144 + x^2-144 = 169-144 ... subtract 144 from both sides x^2 = 25 sqrt(x^2) = sqrt(25) ... apply square root to both sides x = 5
Side Note: Keep in mind that x can't be negative so it doesn't make sense to use the plus/minus here. We'll only stick with the positive version.
