To find the height of the Great Pyramid of Giza, we can use the Pythagorean theorem. The height, the half of the base length, and the slant height form a right triangle.
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The length of the edge of the base (side of the square) is 230.5 m.
- Half of the base length (a) is: \[ a = \frac{230.5}{2} = 115.25 , \text{m} \]
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Let \( h \) be the height of the pyramid, and the slant height (l) is given as 180.2 m. According to the Pythagorean theorem: \[ l^2 = h^2 + a^2 \]
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Plugging in the values: \[ (180.2)^2 = h^2 + (115.25)^2 \] \[ 32472.04 = h^2 + 13270.5625 \]
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Now, solve for \( h^2 \): \[ h^2 = 32472.04 - 13270.5625 \] \[ h^2 = 19201.4775 \]
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Taking the square root to find \( h \): \[ h = \sqrt{19201.4775} \approx 138.6 , \text{m} \]
Rounded to the nearest tenth, the height of the pyramid is approximately 138.6 m.