Final answer:
To solve for the length of the ladder needed to reach a height of 9 feet with its base 3 feet from the wall, we apply the Pythagorean theorem, resulting in a ladder length of √90, which is approximately 9.49 feet.
Step-by-step explanation:
The question provided requires the application of concepts from statics within Physics to determine the length of a ladder needed to reach a certain height against a wall. Since the ladder needs to rest against the wall at a height of 9 feet, and the foot of the ladder will be 3 feet from the wall, we can use the Pythagorean theorem to find the length of the ladder.
To find the necessary length of the ladder, L, we apply the theorem to the right-angled triangle formed by the wall, ground, and the ladder:
L^2 = height^2 + base^2
Substituting the known values:
L^2 = 9^2 + 3^2
L^2 = 81 + 9
L^2 = 90
Taking the square root of both sides, we find:
L = √90
So the ladder length L is √90, which is approximately 9.49 feet. However, for safety and practicality, a slightly longer ladder would likely be used in the real world.