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 your answer to the nearest tenth
To find the height of the pyramid, we can use the Pythagorean theorem. In a right triangle, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
Let's denote the height of the pyramid as "h."
Using the given information, we can set up the following equation:
h^2 + (230.5/2)^2 = (180.2)^2
Simplifying this equation:
h^2 + 53402.25 = 32544.04
Subtracting 53402.25 from both sides:
h^2 = 32544.04 - 53402.25
h^2 = 20858.21
To find h, we take the square root of both sides to eliminate the exponent:
h ≈ √20858.21
h ≈ 144.3
Rounding the answer to the nearest tenth, the height of the pyramid is approximately 144.3 meters.