To find out how far the stake needs to be from the middle of the tent, we can visualize the situation as a right triangle. The height of the tent where the rope attaches is 4 feet above the ground, and the length of the rope is 8 feet.
In this triangle:
- One leg represents the height from the ground to the point where the rope is attached (4 feet).
- The hypotenuse represents the length of the rope (8 feet).
- The other leg represents the horizontal distance from the base of the tent to the stake, which is what we want to find.
Using the Pythagorean theorem, we have: \[ a^2 + b^2 = c^2 \] where:
- \( a \) is the height (4 feet),
- \( b \) is the horizontal distance (the unknown),
- \( c \) is the length of the rope (8 feet).
Substituting the known values: \[ 4^2 + b^2 = 8^2 \] \[ 16 + b^2 = 64 \] Now, we isolate \( b^2 \): \[ b^2 = 64 - 16 \] \[ b^2 = 48 \] Now, taking the square root of both sides: \[ b = \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \approx 6.93 \]
Thus, the stake needs to be approximately 6.93 feet from the middle of the tent.
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