To find the height of a square pyramid (the circus tent in this case) with a square base and known slant height, we can use the Pythagorean theorem.
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Identify the elements:
- The length of each edge of the square base \( a = 20 \) m.
- The slant height \( l = 13.5 \) m.
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Calculate the length of the half base edge:
- Half of the base edge is: \[ \frac{a}{2} = \frac{20}{2} = 10 \text{ m} \]
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Use the Pythagorean theorem: The slant height \( l \), the height \( h \) of the pyramid, and half of the base edge form a right triangle. Using the Pythagorean theorem: \[ l^2 = h^2 + \left(\frac{a}{2}\right)^2 \]
Substituting the known values: \[ (13.5)^2 = h^2 + (10)^2 \]
This simplifies to: \[ 182.25 = h^2 + 100 \]
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Solve for \( h^2 \): \[ h^2 = 182.25 - 100 \] \[ h^2 = 82.25 \]
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Find \( h \): \[ h = \sqrt{82.25} \approx 9.1 \text{ m} \]
Therefore, the height of the tent, rounded to the nearest tenth, is approximately \( \boxed{9.1} \) meters.
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