The height of the Great Pyramid of Giza, calculated using the square base edge length and slant height, is approximately 76.9 meters.
Find the height of the Great Pyramid of Giza, given its square base edge length and slant height:
1: Calculate the half base diagonal.
We can use the Pythagorean theorem to find the length of half the base diagonal. Since the base is a square, the diagonal will be √2 times the base edge length. Therefore:
Half base diagonal = √(base edge length^2 / 2) = √(230.5 m^2 / 2) ≈ 162.9 m
2: Calculate the height of the pyramid.
Now, we can use the slant height and half base diagonal to find the height of the pyramid. Remember that the pyramid forms a right triangle with the slant height as the hypotenuse and half the base diagonal as one leg. The height of the pyramid is the other leg. Therefore:
Height = √(slant height^2 - half base diagonal^2) = √(180.2 m^2 - 162.9 m^2) ≈ 76.9 m
3: Round the answer.
Rounding the height to the nearest tenth gives:
Height ≈ 76.9 m
Therefore, the height of the Great Pyramid of Giza is approximately 76.9 meters.