The ladder, wall, and the floor makes a right triangle with the hypotenuse equal to the length of the ladder. Let h be the height in the wall of the barn that the ladder reached and applying the Pythagorean theorem,
(12 ft)² = h² + (3 ft)²
The value of h is equal to 11.62 ft. Thus, the ladder reached up to 11.62 ft of the wall.