The great pyramid of Giza in Egypt has a square base with edge length of 230.5 m in a slant height of 180.2 m by the height of the pyramid around the answers to the nearest tenth
To find the height of the pyramid, we can use the Pythagorean theorem.
The slant height (180.2 m) represents the hypotenuse of a right triangle, with the height (h) as one of the legs and half the length of the base (230.5/2 = 115.25 m) as the other leg.
Using the Pythagorean theorem:
h^2 + (115.25)^2 = (180.2)^2
Simplifying the equation:
h^2 = (180.2)^2 - (115.25)^2
h^2 = 32472.04 - 13302.56
h^2 = 19169.48
Taking the square root of both sides to solve for h:
h ≈ √19169.48
h ≈ 138.5
Therefore, the height of the pyramid is approximately 138.5 meters.
To find the height of the pyramid, we can use the Pythagorean theorem.
The slant height of the pyramid (l) is the hypotenuse of a right triangle, with the base length (b) as one of the legs and the height (h) as the other leg.
Using the Pythagorean theorem, we have:
l^2 = b^2 + h^2
Substituting the given values:
(180.2 m)^2 = (230.5 m)^2 + h^2
Now, let's solve for h:
h^2 = (180.2 m)^2 - (230.5 m)^2
h^2 = 32544.04 m^2 - 53252.25 m^2
h^2 = - 20708.21 m^2 (Note: we have a negative value because 230.5 m is less than 180.2 m, indicating an invalid triangle in this context)
Since we cannot have a negative height for the pyramid, it seems that there may have been an error in one of the given measurements. Please double-check the values provided to ensure accuracy.
To find the height of the pyramid, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (slant height) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the slant height of the pyramid is 180.2 m and the base of the pyramid is a square with an edge length of 230.5 m. To find the height (h) of the pyramid, we can set up the following equation:
h^2 = (slant height)^2 - (base edge length/2)^2
Plugging in the given values, we get:
h^2 = 180.2^2 - (230.5/2)^2
Calculating this equation gives us:
h^2 = 32544.04 - 26585.25
h^2 = 5962.79
Taking the square root of both sides, we find:
h ≈ √5962.79
h ≈ 77.1 (rounded to the nearest tenth)
Therefore, the height of the pyramid is approximately 77.1 meters.