The Great Pyramid of Cheops in Giza, Egypt, was completed around 2566 B.C.E. Its original height was 482 ft. Each face of the pyramid forms a 52 degree angle with the ground. To the nearest foot, how long is the base of the pyramid?
Draw a triangle ABC with A at the center of the base, B at the tip of the pyramid, and C at the middle of one side.
Then AC = 482 * cot 52
AC is also half the length of a base side.
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To find the length of the base of the Great Pyramid of Cheops in Giza, we can use trigonometry and the given information about the height and the angle formed by each face with the ground.
Let's consider one face of the pyramid as a right triangle, with the height of 482 ft being the height of the triangle, and the base of the triangle being the length we want to find, let's call it "x".
In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the pyramid (482 ft) and the adjacent side is half of the base of the pyramid (x/2), as each face forms an angle with the ground.
Using trigonometry, we can calculate the length of the base "x" by finding the length of the adjacent side:
tan(angle) = opposite side / adjacent side
tan(52 degrees) = 482 ft / (x/2)
To solve for "x", we can rearrange the equation:
tan(52 degrees) = 482 ft / (x/2)
2 * tan(52 degrees) = 482 ft / x
x = (482 ft) / (2 * tan(52 degrees))
Now let's plug in the values and calculate:
x = (482 ft) / (2 * tan(52 degrees))
x = (482 ft) / (2 * 1.2799416321936397) (using the tangent of 52 degrees, which is approximately 1.2799416321936397)
x ≈ (482 ft) / 2.5598832643872793
x ≈ 188.476 ft
So, to the nearest foot, the length of the base of the Great Pyramid of Cheops is approximately 188 ft.