This is a problem involving the Pythagorean theorem, since it deals with right triangles formed by the ladder, the fence, and the horizontal distance from the ladder to the fence.

Problem breakdown:

• The ladder is placed 11 feet from the fence.
• The fence is 12 feet high.
• The building is 1 foot away from the fence, and the window is 15 feet high. The ladder will rest against the building at a height of 15 feet (3 feet above the fence).

Approach:

The situation forms two right triangles:

1. The first triangle has:

   • Height: 12 feet (height of the fence)
   • Base: 11 feet (horizontal distance to the fence)

   Using the Pythagorean theorem, the length of the ladder from the ground to the top of the fence can be calculated.

2. The second triangle represents the part of the ladder that extends beyond the fence:

   • Height: 3 feet (15 feet - 12 feet)
   • Base: 1 foot (distance from fence to building)

We can calculate the length of the ladder using these two right triangles.

Let's calculate the total length of the ladder.The total length of the ladder needed is approximately 19.4 feet, rounded to the nearest tenth of a foot.

Would you like more details, or do you have any questions?

Here are five related questions to explore:

1. How would the ladder's length change if the window was higher or lower than 15 feet?
2. How does increasing the distance from the fence affect the length of the ladder?
3. Could the ladder be placed at a different distance from the fence and still reach the window?
4. What if the building was more than 1 foot away from the fence—how would that affect the ladder's length?
5. How can the Pythagorean theorem be applied in other real-world scenarios like this?

Tip: When dealing with right triangles, always try to visualize and break the problem into smaller triangles, applying the Pythagorean theorem step by step.