To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The pyramid has a square base and forms a right triangle when we look at a vertical cross-section that runs through the apex and the center of one side of the base.
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The base of the triangle (half of the base edge length) is: \[ \text{half base} = \frac{230.5}{2} = 115.25 \text{ m} \]
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The slant height is given as: \[ \text{slant height} = 180.2 \text{ m} \]
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We need to find the height \( h \) of the pyramid. According to the Pythagorean theorem, we have the equation: \[ \text{slant height}^2 = \text{half base}^2 + h^2 \]
Plugging in the values: \[ (180.2)^2 = (115.25)^2 + h^2 \]
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Now we calculate the squares: \[ 180.2^2 = 32472.04 \quad \text{and} \quad 115.25^2 = 13274.0625 \]
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Now substitute these values back into the equation: \[ 32472.04 = 13274.0625 + h^2 \]
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Now isolate \( h^2 \): \[ h^2 = 32472.04 - 13274.0625 = 19197.9775 \]
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Take the square root to find \( h \): \[ h = \sqrt{19197.9775} \approx 138.6 \text{ m} \]
Therefore, the height of the Great Pyramid of Giza is approximately 138.6 m when rounded to the nearest tenth.