Final answer:
To find the length of the shortest ladder that will reach from the ground over a 3-foot fence to a wall 5 feet away, apply the Pythagorean theorem. The length of the ladder is the square root of the sum of the squares of the fence's height and the distance to the building. Thus, the ladder must be approximately 5.83 feet long.
Step-by-step explanation:
The student is asking about a geometry problem related to finding the length of the shortest ladder that can reach from the ground over a fence to a building. This is a classic application of the Pythagorean theorem, which states that in a right-angled 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 lengths of the other two sides (the legs).
To solve for the length of the ladder, which serves as the hypotenuse in this scenario, we will consider the distance from the fence to the building and the height of the fence as the two legs of a right triangle. The ladder must extend beyond the height of the fence by reaching over it to the wall, forming a right triangle with the ground and the fence.
Let us denote the length of the ladder as 'L', the distance from the fence to the building (5 feet) as 'D', and the height of the fence (3 feet) as 'H'. Using the Pythagorean theorem:
L2 = H2 + D2
L2 = 32 + 52
L2 = 9 + 25
L2 = 34
L = √34
L ≈ 5.83 feet (rounded to two decimal places)
Therefore, the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 5.83 feet long.