Bot GPT 4-o mini To find the height of the square pyramid (circus tent), we can use the Pythagorean theorem. The slant height (l) of the pyramid forms a right triangle with the height (h) of the pyramid and half the length of the base (b/2).
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Find the half-base length: The length of each edge of the square base is 20 m, so: \[ b = 20 \text{ m} \] Half of the base length is: \[ \frac{b}{2} = \frac{20}{2} = 10 \text{ m} \]
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Use the Pythagorean theorem: The relationship between the height (h), the slant height (l), and half the base length is given by: \[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \] Plugging in the values: \[ 13.5^2 = h^2 + 10^2 \]
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Calculate: \[ 182.25 = h^2 + 100 \] \[ h^2 = 182.25 - 100 = 82.25 \] \[ h = \sqrt{82.25} \approx 9.1 \text{ m} \]
Thus, the height of the tent is approximately 9.1 m.
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