The great oyramid 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. Let's call the height of the pyramid "h". We know that the slant height is 180.2 m and the base edge length is 230.5 m.
Using the Pythagorean theorem, we have:
h^2 + (230.5/2)^2 = 180.2^2
Simplifying, we get:
h^2 + 26535.25 = 32544.04
h^2 = 6008.79
Taking the square root of both sides to solve for h, we get:
h ≈ 77.6 m
Therefore, the height of the pyramid is approximately 77.6 meters.
Keysha is building a coffee table. its going to be the shape of a rectangular prism, without the face. she wants to make the table decorative by adding metal diagonals. the lenth 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
To find the length of each diagonal, we can use the Pythagorean theorem. Let's call the length, width, and height of the coffee table L, W, and H, respectively.
L = 44 in.
W = 24 in.
H = 14 in.
To find the length of the diagonal, let's consider the diagonal of the rectangular prism as the hypotenuse of a right triangle. We can use the formula:
diagonal^2 = length^2 + width^2 + height^2
Plugging in the values:
diagonal^2 = (44 in.)^2 + (24 in.)^2 + (14 in.)^2
diagonal^2 = 1936 in^2 + 576 in^2 + 196 in^2
diagonal^2 = 2708 in^2
Taking the square root of both sides to solve for the diagonal, we get:
diagonal ≈ 52.0 in.
Therefore, Keysha should make each diagonal approximately 52.0 inches long.
To find the height of the pyramid, we can use the Pythagorean theorem in the right triangle formed by the height, half of the base, and the slant height.
The Pythagorean theorem states that in a right triangle, the square 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, and half of the base is one of the sides. Let's call the height "h," the half of the base "b," and the slant height "s."
According to the Pythagorean theorem, we have:
s^2 = b^2 + h^2
Given that the edge length of the square base is 230.5 m, half of the base (b) is 230.5 / 2 = 115.25 m. The slant height (s) is given as 180.2 m.
Plugging these values into the equation, we get:
180.2^2 = 115.25^2 + h^2
Simplifying:
32,484.04 = 13,263.06 + h^2
Subtracting 13,263.06 from both sides:
19,220.98 = h^2
To find the height (h), we can take the square root of both sides:
√19,220.98 ≈ 138.7
Therefore, the height of the pyramid is approximately 138.7 meters when rounded to the nearest tenth.