To find the height of the square pyramid (circus tent), we can use the Pythagorean theorem.
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The base of the pyramid is a square with each edge measuring 20 m. This means the half-length of the base, which we will call \(a\), is: \[ a = \frac{20}{2} = 10 \text{ m} \]
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The slant height of the pyramid (the height of the triangular face) is given as 13.5 m. We will denote this slant height as \(l\).
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Let's denote the height of the pyramid as \(h\).
According to the Pythagorean theorem, we can relate the height, the half-base, and the slant height as follows: \[ l^2 = h^2 + a^2 \]
Substituting in the known values: \[ (13.5)^2 = h^2 + (10)^2 \]
Calculating \(13.5^2\) and \(10^2\): \[ 182.25 = h^2 + 100 \]
Now, isolate \(h^2\): \[ h^2 = 182.25 - 100 \] \[ h^2 = 82.25 \]
Taking the square root to find \(h\): \[ h = \sqrt{82.25} \approx 9.065 \]
Rounding to the nearest tenth: \[ h \approx 9.1 \text{ m} \]
Thus, the height of the tent is 9.1 m.
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