Final answer:
By applying the Pythagorean theorem with the given measurements, we find that the base of the ladder should be approximately 12.04 feet from the wall, making 13 feet the closest given answer.
Step-by-step explanation:
If a roof is 12 feet off the ground, and the ladder is 17 feet, we can determine how far away the base of the ladder should be placed by using the Pythagorean theorem. According to the theorem, c² = a² + b², where c is the length of the ladder, a is the distance from the base of the ladder to the wall, and b is the height the ladder reaches on the wall. Substituting the known values, we get 17² = a² + 12², which simplifies to 289 = a² + 144. Subtracting 144 from both sides gives us a² = 145, thus a is approximately 12.04 feet. The closest answer from the options given is b) 13 feet.