This is a classic example of a right triangle problem, where the ladder is the hypotenuse of the right triangle, and the base of the building and the height to which the ladder reaches are the other two sides.
We can use the Pythagorean theorem to solve for the height:
a^2 + b^2 = c^2
where a and b are the lengths of the two shorter sides (the base and the height), and c is the length of the hypotenuse (the ladder).
Plugging in the values we know, we get:
3^2 + b^2 = 12^2
9 + b^2 = 144
b^2 = 135
b ≈ 11.62
Rounding to the nearest whole number, we get:
The ladder reaches approximately 12 feet up the side of the building.