To find the height of the circus tent, which is shaped like a square pyramid, we can use the Pythagorean theorem. In a square pyramid, the height, the slant height, and half of the base edge form a right triangle.
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Identify the dimensions:
- Base edge (side length of the square base) = 20 meters
- Half of the base edge = \( \frac{20}{2} = 10 \) meters
- Slant height = 13.5 meters
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Set up the Pythagorean theorem: Let \( h \) be the height of the pyramid. According to the Pythagorean theorem: \[ \text{slant height}^2 = \text{height}^2 + \left(\frac{\text{base edge}}{2}\right)^2 \] Substituting the values we have: \[ 13.5^2 = h^2 + 10^2 \]
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Calculate \( 13.5^2 \) and \( 10^2 \): \[ 13.5^2 = 182.25 \] \[ 10^2 = 100 \]
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Plug these values into the equation: \[ 182.25 = h^2 + 100 \]
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Solve for \( h^2 \): \[ h^2 = 182.25 - 100 = 82.25 \]
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Find \( h \): \[ h = \sqrt{82.25} \approx 9.065 \]
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Round to the nearest tenth: \[ h \approx 9.1 \text{ meters} \]
Thus, the height of the tent is approximately 9.1 meters.
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