To find the height of the pyramid, we can use the Pythagorean theorem. The pyramid has a square base, which means the height, the slant height, and half the base edge length form a right triangle.
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Determine half the length of the base edge: \[ \text{Half base edge} = \frac{\text{Edge length}}{2} = \frac{202.5 \text{ yds}}{2} = 101.25 \text{ yds} \]
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Set up the Pythagorean theorem: \[ \text{slant height}^2 = \text{height}^2 + \left(\text{Half base edge}\right)^2 \] Let \( h \) be the height of the pyramid: \[ 175.1^2 = h^2 + 101.25^2 \]
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Calculate \( 175.1^2 \) and \( 101.25^2 \): \[ 175.1^2 = 30645.01 \] \[ 101.25^2 = 10253.0625 \]
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Substituting into the equation: \[ 30645.01 = h^2 + 10253.0625 \]
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Solving for \( h^2 \): \[ h^2 = 30645.01 - 10253.0625 \] \[ h^2 = 20391.9475 \]
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Taking the square root to find \( h \): \[ h = \sqrt{20391.9475} \approx 142.0 \text{ yds} \]
Therefore, the height of the pyramid rounded to the nearest tenth is 142.0 yards.