Bot GPT 4-o mini To find the height of a square pyramid (the circus tent in this case), we can use the relationship between the height \( h \), the slant height \( l \), and half the base edge \( a \).
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Identify the given values:
- Base edge \( a = 20 \) meters
- Slant height \( l = 13.5 \) meters
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Calculate half the base edge: \[ \frac{a}{2} = \frac{20}{2} = 10 \text{ meters} \]
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Using the Pythagorean theorem: In a right triangle formed by the height \( h \), half the base edge \( \frac{a}{2} \), and the slant height \( l \): \[ l^2 = h^2 + \left(\frac{a}{2}\right)^2 \] Plugging in the known values: \[ 13.5^2 = h^2 + 10^2 \] This simplifies to: \[ 182.25 = h^2 + 100 \]
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Rearranging to find \( h^2 \): \[ h^2 = 182.25 - 100 = 82.25 \]
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Taking the square root to find \( h \): \[ h = \sqrt{82.25} \approx 9.1 \]
Thus, the height of the tent, rounded to the nearest tenth, is approximately 9.1 meters.
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