To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The pyramid has a square base, which means that from the center of the base to a corner of the base forms the base of a right triangle where the slant height is the hypotenuse, and the height of the pyramid is one of the other sides.
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Calculate the half-length of the base: The length of one side of the base is 230.5 m, therefore half of this length (the distance from the center of the base to a corner) is: \[ \text{Half base} = \frac{230.5}{2} = 115.25 \text{ m} \]
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Use Pythagorean theorem: Let \( h \) denote the height of the pyramid. By the Pythagorean theorem: \[ h^2 + (115.25)^2 = (180.2)^2 \]
Plugging in the values: \[ h^2 + 115.25^2 = 180.2^2 \] Calculate \( 115.25^2 \): \[ 115.25^2 = 13276.5625 \]
Calculate \( 180.2^2 \): \[ 180.2^2 = 32472.04 \]
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Substitute and solve for \( h^2 \): \[ h^2 + 13276.5625 = 32472.04 \] \[ h^2 = 32472.04 - 13276.5625 \] \[ h^2 = 19195.4775 \]
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Take the square root to find \( h \): \[ h = \sqrt{19195.4775} \approx 138.66 \]
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Round to the nearest tenth: The height of the pyramid is approximately: \[ \boxed{138.7 \text{ m}} \]
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