To find the height of the square pyramid (circus tent), we can use the Pythagorean theorem. The height \( h \), the slant height \( l \), and the distance from the center of the base to the midpoint of one edge (half the length of the base) form a right triangle.
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Calculate the half of the base edge: \[ \text{Half of base edge} = \frac{20 \text{ m}}{2} = 10 \text{ m} \]
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Use the Pythagorean theorem: \[ l^2 = h^2 + \left(\frac{\text{base edge}}{2}\right)^2 \] Where:
- \( l = 13.5 \) m (slant height)
- Base edge = 20 m
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Substituting the values: \[ 13.5^2 = h^2 + 10^2 \] \[ 182.25 = h^2 + 100 \]
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Rearranging the equation to solve for \( h^2 \): \[ h^2 = 182.25 - 100 \] \[ h^2 = 82.25 \]
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Taking the square root of both sides to find \( h \): \[ h = \sqrt{82.25} \approx 9.1 \text{ m} \]
Thus, the height of the tent rounded to the nearest tenth is:
9.1 m.
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