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(point )
To find the height of the pyramid, we can use the Pythagorean theorem.
Let's call the height of the pyramid h.
We can create a right triangle using the slant height, height, and half the base.
The slant height is given as 180.2 m.
Half the base is given by dividing the edge length by 2: 230.5 / 2 = 115.25 m.
Using the Pythagorean theorem, we have:
h^2 + 115.25^2 = 180.2^2.
Simplifying, we get:
h^2 + 13253.0625 = 32472.04.
Subtracting 13253.0625 from both sides, we have:
h^2 = 19218.9775.
Taking the square root of both sides, we find:
h ≈ 138.7.
Rounding to the nearest tenth, the height of the pyramid is approximately 138.7 m.