Final answer:
The length of the ladder is 20 feet.
Step-by-step explanation:
To find the length of the ladder, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the ladder forms a right triangle with the roof and the ground as the other two sides.
Let's label the length of the ladder as L, the height of the roof as H, and the distance from the base of the ladder to the house as D.
Since we know H = 16 feet and D = 12 feet, we can use the Pythagorean theorem to find L.
L^2 = D^2 + H^2
L^2 = 12^2 + 16^2
L^2 = 144 + 256
L^2 = 400
L = sqrt(400)
L = 20 feet
Therefore, the length of the ladder is 20 feet.