Final answer:
The top of the ladder moves down the wall by approximately 1.75 feet when the base of the ladder is pulled out an additional 3 feet from the wall, as calculated using the Pythagorean theorem.
Step-by-step explanation:
To determine how far the top of the ladder moves down the wall when its base is pulled out, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The ladder forms a right triangle with the ground and the wall. In this scenario, the ladder's length is the hypotenese, and it does not change. Initially, the ladder is 5 feet from the wall. When it's pulled 3 feet farther out, it becomes 8 feet from the wall.
Originally, we have:
c2 = a2 + b2132 = 52 + b2
169 = 25 + b2
144 = b2
b = −12 = 12 (since b represents a length, it cannot be negative)
After pulling out the base:
169 = 82 + b'2
169 = 64 + b'2
105 = b'2
b' = −105 ≈ 10.25
Therefore, the top of the ladder moves down the wall by about:
Original height - New height = 12 ft - 10.25 ft ≈ 1.75 ft
The correct answer is b. approximately 1.75 ft.