The Great Pyramid of Giza in Egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. Find the height of the pyramid. Round to the nearest tenth.
To find the height of the pyramid, we can use the Pythagorean theorem.
The slant height of the pyramid (180.2 m) can be seen as the hypotenuse of a right triangle, with the base of the triangle being half the length of the square base of the pyramid (230.5 m).
Let's call the height of the pyramid "h". Using the Pythagorean theorem, we can write:
h^2 + (half the base)^2 = slant height^2
h^2 + (230.5/2)^2 = 180.2^2
h^2 + 115.25^2 = 180.2^2
h^2 + 13267.0625 = 32472.04
h^2 = 19204.9775
h ≈ √19204.9775
h ≈ 138.7
Therefore, the height of the pyramid is approximately 138.7 m. Rounding to the nearest tenth, the height is 138.7 m.