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The problem you've uploaded involves the Pythagorean Theorem, which is used to find the length of a side in a right triangle. The ladder represents the hypotenuse, while the height and the distance from the wall represent the two legs of the triangle.

### Problem Breakdown:
1. **Ladder Length (Hypotenuse)**: 7 meters.
2. **Height of Ladder from the Ground**: \(x\) meters.
3. **Distance of the Ladder Base from the Wall**: \(y\) meters.

### Pythagorean Theorem:
The theorem states that in a right-angled triangle:

\[
\text{Hypotenuse}^2 = \text{Height}^2 + \text{Base}^2
\]

This can be written as:

\[
7^2 = x^2 + y^2
\]

Given that \( y = 4 \) meters (the distance from the wall), we substitute into the equation:

\[
7^2 = x^2 + 4^2
\]

\[
49 = x^2 + 16
\]

### Solve for \( x \):

\[
x^2 = 49 - 16 = 33
\]

\[
x = \sqrt{33} \approx 5.74 \text{ meters}
\]

Thus, the ladder is approximately **5.74 meters** high on the wall.

Would you like any further details on this solution, or do you have any other questions?

Here are 5 questions that expand on this information:
1. How does the Pythagorean Theorem apply to real-world scenarios beyond this ladder problem?
2. What would happen to the height if the distance from the wall increased?
3. Can you use the Pythagorean Theorem to determine the length of any side if two sides are known?
4. How does the accuracy of measurement affect the application of the Pythagorean Theorem?
5. How would you calculate the angle of elevation of the ladder?

**Tip:** Remember that the Pythagorean Theorem only applies to right-angled triangles. If you encounter non-right triangles, you'll need to use other trigonometric methods.

The foot of a ladder is placed 4 meters from a wall. If the top of the ladder rests 7 meters up on the wall, how long is the ladder?

Learn how to calculate the height of a ladder leaning against a wall using the Pythagorean Theorem. This detailed solution breaks down the right triangle formed by the ladder, wall, and ground. Suitable for students in Grades 8-10.

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