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.
The slant height of the pyramid is the hypotenuse of a right triangle, with the height of the pyramid as one leg and half of the base length of the pyramid as the other leg.
Let's call the height of the pyramid "h", and half of the base length "b". We have the following equation:
h^2 + b^2 = slant height^2
We know that the edge length of the square base is 230.5 m, so half of the base length (b) is 230.5/2 = 115.25 m.
Plugging in the values, we get:
h^2 + 115.25^2 = 180.2^2
Simplifying:
h^2 + 13260.0625 = 32472.04
h^2 = 32472.04 - 13260.0625
h^2 = 19211.9775
Taking the square root of both sides, we get:
h = sqrt(19211.9775)
h ≈ 138.7
Therefore, the height of the pyramid is approximately 138.7 meters.