To find the height of the tent (the square pyramid), we can use the relationship between the height, the slant height, and the half of the base edge.
Given:
- Edge of the square base \( b = 20 , \text{m} \)
- Slant height \( l = 13.5 , \text{m} \)
Steps:
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Find the half of the base edge: Since the base is a square, the half of the edge length is: \[ \frac{b}{2} = \frac{20}{2} = 10 , \text{m} \]
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Use the Pythagorean theorem: In a right triangle formed by the height \( h \), the half of the base edge, and the slant height, we have: \[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \] Substituting the values: \[ 13.5^2 = h^2 + 10^2 \] \[ 182.25 = h^2 + 100 \]
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Solve for \( h^2 \): \[ h^2 = 182.25 - 100 = 82.25 \] Then, take the square root: \[ h = \sqrt{82.25} \approx 9.1 , \text{m} \]
Final Answer:
The height of the tent rounded to the nearest tenth is approximately 9.1 m.
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