To solve the problem of determining the length of the ladder, we can assume the following typical scenario based on the given image:

- A ladder is leaning against a building, forming a right triangle with the wall (the height) and the ground (the distance from the wall).
- You have the distance from the bottom of the ladder to the building as one side of the triangle, and the height that the ladder reaches on the wall as the other side.

Let:
- \( d \) be the distance from the base of the building to the bottom of the ladder (horizontal distance).
- \( h \) be the height that the ladder reaches on the wall (vertical distance).
- \( L \) be the length of the ladder.

Using the Pythagorean theorem:

\[
L = \sqrt{d^2 + h^2}
\]

### Step-by-Step Solution:

1. **Distance from the wall (horizontal distance):** \( d = 6 \) feet (as given in the problem).
2. **Height on the wall (vertical distance):** \( h = 8 \) feet (as given in the problem).

Now, apply the Pythagorean theorem:

\[
L = \sqrt{6^2 + 8^2}
\]

\[
L = \sqrt{36 + 64}
\]

\[
L = \sqrt{100}
\]

\[
L = 10 \text{ feet}
\]

### Answer:
The length of the ladder is **10 feet**.

If you have further questions or need more details, feel free to ask! Here are some related questions:

1. How would the length of the ladder change if the distance from the wall increased?
2. Can you calculate the angle of elevation of the ladder using trigonometric functions?
3. What happens to the ladder length if the height increases but the distance remains the same?
4. How would you solve for the height if only the ladder length and distance from the wall are known?
5. What if the ladder slips and the base moves closer or farther from the wall?
6. How can you determine the maximum safe angle for the ladder to prevent slipping?
7. What if the wall is not vertical—how does this affect the problem?
8. How do you solve problems involving ladders on uneven ground?

**Tip:** When dealing with right triangles, always consider whether the problem might require you to calculate the missing side or the angle using trigonometric ratios.

Learn how to calculate the length of a ladder leaning against a building using the Pythagorean theorem. This problem involves determining the length of the ladder given the horizontal distance from the building and the height on the wall. Suitable for students in Grades 7-9.

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