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 the answer to the nearest tenth
To find the height of the pyramid, we can use the Pythagorean Theorem. Let's consider a right triangle with one side being the height of the pyramid, the other side being half the length of the base (since the base is square), and the hypotenuse being the slant height of the pyramid.
We know that the length of one side of the base is 230.5 m, so half the length of the base is 230.5/2 = <<230.5/2=115.25>>115.25 m.
Let h be the height of the pyramid. Using the Pythagorean Theorem, we have:
h^2 + (115.25)^2 = (180.2)^2
Simplifying the equation:
h^2 + 13260.0625 = 32544.04
h^2 = 32544.04 - 13260.0625
h^2 = 19283.9775
Taking the square root of both sides:
h ≈ √19283.9775
h ≈ 138.8
Therefore, the height of the pyramid is approximately 138.8 m. Rounding to the nearest tenth, the height is 138.8 m.