To find the height of the Great Pyramid of Giza, we can apply the Pythagorean theorem. The slant height, the height of the pyramid, and half the length of the base form a right triangle.
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First, calculate half the length of the base: \[ \text{Half of base} = \frac{230.5}{2} = 115.25 \text{ m} \]
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We know the slant height (the hypotenuse \( s \)) is 180.2 m, and we want to find the height (let's call it \( h \)) of the pyramid. We can use the Pythagorean theorem: \[ s^2 = h^2 + \left(\frac{b}{2}\right)^2 \] Plugging in the values: \[ (180.2)^2 = h^2 + (115.25)^2 \]
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Calculate \( (180.2)^2 \) and \( (115.25)^2 \): \[ (180.2)^2 = 32544.04 \] \[ (115.25)^2 = 13276.0625 \]
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Substitute back into the equation: \[ 32544.04 = h^2 + 13276.0625 \]
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Rearranging to solve for \( h^2 \): \[ h^2 = 32544.04 - 13276.0625 = 19267.9775 \]
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Take the square root of both sides to find \( h \): \[ h = \sqrt{19267.9775} \approx 138.8 \text{ m} \]
Rounding to the nearest tenth, the height of the pyramid is approximately 138.8 m.