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)

Question

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)

m

Answer 1

To find the height of the pyramid, we can use the Pythagorean Theorem.

The slant height of the pyramid, h, the height of the pyramid, and the half-length of the base, 230.5/2 = 115.25 m, form a right triangle.

Using the Pythagorean Theorem, we have:

h^2 = (115.25)^2 + (180.2)^2

Calculating this value, we get:

h^2 = 13290.0625 + 32568.04

h^2 = 45858.1025

Taking the square root of both sides, we find:

h ≈ √45858.1025

h ≈ 214.2

Therefore, the height of the pyramid is approximately 214.2 meters.

Answer 2

To find the height of the pyramid, we can use the Pythagorean theorem.

The slant height, base, and height form a right triangle.
The base is the length of one side of the triangle, which is 230.5 m.
The slant height is the hypotenuse of the triangle, which is 180.2 m.

Let h be the height of the pyramid.

Using the Pythagorean theorem, we have:
h^2 + 230.5^2 = 180.2^2

Simplifying, we get:
h^2 + 53002.5 = 32472.04

Subtracting 53002.5 from both sides, we get:
h^2 = 32472.04 - 53002.5
h^2 = -19530.46

Taking the square root of both sides, we get:
h = √(-19530.46)

Since we can't take the square root of a negative number, the height of the pyramid is not real.

Therefore, there is no solution for the height of the pyramid.

Answer 3

To find the height of the pyramid, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the slant height is the hypotenuse of a right triangle formed by the height of the pyramid, the slant height, and half of the base of the pyramid. Let's call the height of the pyramid "h".

According to the Pythagorean Theorem, we have:

h^2 + (0.5 * 230.5)^2 = 180.2^2

Simplifying this equation, we get:

h^2 + 26546.125 = 32544.04

Subtracting 26546.125 from both sides, we have:

h^2 = 32544.04 - 26546.125

h^2 = 5997.915

To find the height, we take the square root of both sides:

h = √5997.915

Using a calculator, we find that the approximate height of the pyramid is 77.4 meters (rounded to the nearest tenth).