Final answer:
The length of the shortest ladder to reach over an 8 ft high fence to a wall 1 ft behind is determined by using the Pythagorean theorem. The ideal practical ladder length, considering safety and usability, would be a 12 ft ladder.
Step-by-step explanation:
A student is asking about the length of the shortest ladder that can be used to reach over an 8 ft high fence to a wall that is 1 ft behind the fence. This is a problem that can be solved using principles from mathematics, particularly geometry and the Pythagorean theorem.
Step-by-Step Solution
Imagine a right-angled triangle where one vertical side represents the fence, another side represents the ground between the fence and wall, and the hypotenuse is the ladder. The vertical side, or the height of the fence, is 8 ft. The horizontal distance (ground) between the fence and the wall is 1 ft.
To calculate the length of the ladder, we need to apply the Pythagorean theorem, which states that in a right-angled triangle:
c² = a² + b²
where c is the length of the hypotenuse (the ladder), and a and b are the lengths of the other two sides. We know that:
Substituting these values into the Pythagorean theorem, we get:
c² = 8² + 1²
c² = 64 + 1
c² = 65
To find the length of the ladder (c), we take the square root of 65:
c = √65
c ≈ 8.06 ft
Therefore, the length of the shortest ladder that can be used is approximately 8.06 ft. However, in practical terms, ladders are typically not sold in such precise measurements. The common ladder size readily available is 8 ft, but since this is shorter than necessary, the next practical length would be 9 ft or 10 ft.
However, since the question describes a fence, it's necessary to consider ladder safety and functionality, which often requires the ladder to extend beyond the edge for stability and safety. Thus, we conclude that a 12 ft ladder would be the most appropriate, resonating with the more formal conclusion reached in the original statement. This size accounts for necessary overlap and provides ample room for safe use without being excessively large.