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 po
To find the height of the pyramid, we can use the Pythagorean theorem.
The height, the slant height, and half the length of the base form a right triangle.
Let the height of the pyramid be h.
Using the Pythagorean theorem, we have:
(1/2 of the base)^2 + h^2 = slant height^2
(230.5/2)^2 + h^2 = 180.2^2
(115.25)^2 + h^2 = 32544.04
h^2 = 32544.04 - (115.25)^2
h^2 ≈ 32544.04 - 13300.5625
h^2 ≈ 19243.4775
Taking the square root of both sides gives:
h ≈ √19243.4775
h ≈ 138.821
Therefore, the height of the pyramid is approximately 138.8 m.
Keysha is building a coffee table. It’s going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. The length of the coffee table will be 44 in., the width 24 in., and the height 14 in. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth.(1 point)
To find the length of each diagonal, we can use the Pythagorean theorem.
Let's consider the diagonal that goes from one corner of the table to the opposite corner.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (length)^2 + (width)^2 + (height)^2
(diagonal)^2 = (44)^2 + (24)^2 + (14)^2
(diagonal)^2 = 1936 + 576 + 196
(diagonal)^2 = 2708
Taking the square root of both sides gives:
diagonal ≈ √2708
diagonal ≈ 52.04
Therefore, Keysha should make each diagonal approximately 52.0 inches long.