A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
Same as this question, just change the numbers.
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To find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length 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 fence, the building, and the ladder form a right triangle. The fence and the building are the two perpendicular sides, and the ladder is the hypotenuse.
Let's consider the height of the fence (8 ft) as one side of the triangle. The distance from the fence to the building (4 ft) is the other side. We want to find the length of the ladder (hypotenuse).
Using the Pythagorean theorem, we have:
Ladder^2 = Fence^2 + Distance^2
Ladder^2 = 8^2 + 4^2
Ladder^2 = 64 + 16
Ladder^2 = 80
Now, we can solve for the length of the ladder by taking the square root of both sides:
Ladder = √80
Ladder ≈ 8.94 ft
Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 8.94 ft.