To find the height of the tent, we can use the Pythagorean theorem. The rope, the height of the tent, and the distance from the base of the tent to where the rope is staked form a right triangle.
Let:
- \( h \) be the height of the tent,
- \( d \) be the distance from the middle of the tent to where the rope is staked (which is 6 ft),
- \( r \) be the length of the rope (which is 8 ft).
According to the Pythagorean theorem:
\[ h^2 + d^2 = r^2 \]
Substituting the known values into the equation:
\[ h^2 + 6^2 = 8^2 \]
Calculating \( 6^2 \) and \( 8^2 \):
\[ h^2 + 36 = 64 \]
Now, isolate \( h^2 \):
\[ h^2 = 64 - 36 \]
\[ h^2 = 28 \]
Now, take the square root of both sides to find \( h \):
\[ h = \sqrt{28} \]
Which simplifies to:
\[ h = \sqrt{4 \cdot 7} = 2\sqrt{7} \]
Calculating \( 2\sqrt{7} \) gives approximately:
\[ h \approx 5.29 \text{ feet} \]
Therefore, the height of the tent is approximately 5.29 feet.
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