The Great pyramid of Giza in Egypt has a square base with the edge length of 230.5 M and a slant height of 180.2 m. Find the height of the pyramid round the answer to the nearest tenth
To find the height of the pyramid, we can use the Pythagorean theorem.
The slant height (hypotenuse) is the slant height of one of the triangular faces of the pyramid. The height of the pyramid is one of the legs of the right triangle formed by the slant height and half of the base edge length.
Let h be the height of the pyramid.
Using the Pythagorean theorem:
\(180.2^2 = (230.5 / 2)^2 + h^2\)
\(32544.04 = 26600.25 + h^2\)
\(h^2 = 5943.79\)
\(h = \sqrt{5943.79}\)
\(h ≈ 77.1\)
Therefore, the height of the pyramid is approximately 77.1 meters.