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. The height of the pyramid is the square root of the square of the slant height minus the square of half the base.
The square of the slant height is $(180.2)^2 = 32544.04$.
Half of the base is $\frac{230.5}{2} = 115.25$.
The square of half the base is $(115.25)^2 = 13260.0625$.
The height of the pyramid is the square root of $32544.04 - 13260.0625$,
which is $\sqrt{19283.9775} \approx \boxed{139.1}$ meters.
give me an actual number
The height of the pyramid is approximately 139.1 meters, rounded to the nearest tenth.
To find the height of the pyramid, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the pyramid is the hypotenuse, and the base length is one of the other sides. Let's call the height of the pyramid "h."
Using the Pythagorean theorem, we can write the equation:
h^2 + (base length/2)^2 = slant height^2
Substituting the given values:
h^2 + (230.5/2)^2 = 180.2^2
Simplifying:
h^2 + 26531.25 = 32544.04
Now, isolate "h^2" by subtracting 26531.25 from both sides:
h^2 = 32544.04 - 26531.25
h^2 = 6012.79
Finally, take the square root of both sides to solve for "h":
h = √6012.79
Calculating the square root:
h ≈ 77.5
Therefore, the height of the pyramid is approximately 77.5 meters (rounded to the nearest tenth).