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To solve this problem, we’ll analyze the triangle formed by the tent's height, the rope, and the distance from the middle of the tent to the stake.

### Given Data
- The tent height \( h \) = 4 feet (distance from the top of the tent to the ground).
- The rope length (hypotenuse of the triangle) \( c \) = 8 feet.
- We need to find the horizontal distance \( d \) from the middle of the tent to the stake.

### Approach
Since the height of the tent, the rope, and the distance from the tent to the stake form a right triangle, we can use the Pythagorean theorem:
\[
c^2 = h^2 + d^2
\]
Substitute the known values:
\[
8^2 = 4^2 + d^2
\]
\[
64 = 16 + d^2
\]
\[
d^2 = 64 - 16
\]
\[
d^2 = 48
\]
\[
d = \sqrt{48} \approx 6.9 \text{ feet}
\]

### Conclusion
The horizontal distance from the middle of the tent to the stake should be approximately **6.9 feet**.

### Answer
The correct answer is:
- **6.9 feet**

Would you like more details or have any questions about this solution?

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#### Related Questions:
1. How would the distance change if the rope length was increased to 10 feet?
2. What is the formula for the Pythagorean theorem, and when is it applicable?
3. How can trigonometric functions be used to find distances in right triangles?
4. If the height of the tent was 5 feet, how would that affect the distance?
5. How does changing the tent’s height to 3 feet affect the distance calculation?

#### Tip:
Always check if a triangle problem involves a right angle, as it allows you to use the Pythagorean theorem for simple calculations.

A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long, about how far will the stake need to be from the middle of her tent?

Solve a real-world geometry problem by calculating the distance needed to place a stake for a tent using the Pythagorean theorem. With the rope length at 8 feet and the tent height at 4 feet, find the approximate distance to ensure stability.

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