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. (1 point)
To find the height of the pyramid, we can use the Pythagorean theorem.
The slant height is the hypotenuse of a right triangle formed by the height, half of the base length, and the slant height.
So, we have:
height^2 + (base/2)^2 = slant height^2
Let's plug in the given values:
height^2 + (230.5/2)^2 = 180.2^2
height^2 + 53.5^2 = 32544.04
height^2 + 2862.25 = 32544.04
height^2 = 32544.04 - 2862.25
height^2 = 29681.79
Now, we take the square root of both sides:
height = √29681.79
height ≈ 172.1
Therefore, the height of the pyramid is approximately 172.1 meters.