To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The height (h), half of the base length (b/2), and the slant height (l) form a right triangle.
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The base edge length is given as 230.5 m, so half of the base length is: \[ \frac{b}{2} = \frac{230.5}{2} = 115.25 \text{ m} \]
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The slant height (l) is provided as 180.2 m.
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We can now apply the Pythagorean theorem: \[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \] Substituting the known values: \[ 180.2^2 = h^2 + 115.25^2 \]
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This computes to: \[ 180.2^2 = 32472.04 \] \[ 115.25^2 = 13273.5625 \]
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Now plug these values into the equation: \[ 32472.04 = h^2 + 13273.5625 \]
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Rearranging the equation to solve for \(h^2\): \[ h^2 = 32472.04 - 13273.5625 \] \[ h^2 = 19198.4775 \]
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Taking the square root to find \(h\): \[ h = \sqrt{19198.4775} \approx 138.5 \]
So, rounding to the nearest tenth, the height of the pyramid is approximately 138.5 m.