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?

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.