The pyramid is in arena in Memphis Tennessee. It’s height is 321 feet and it’s slant height is 436.5 feet find the length of the edge of the square base around the answer to the nearest 10th.
To find the length of the edge of the square base, we can use the Pythagorean theorem.
Let's call the length of the edge of the square base "x". We can form a right triangle by connecting the height, the slant height, and half of the base diagonal (which is equal to half the length of the edge of the square base).
According to the Pythagorean theorem, the square of the length of the height plus the square of half the base diagonal should equal the square of the slant height.
So, we have:
height^2 + (half the base diagonal)^2 = slant height^2
321^2 + (x/2)^2 = 436.5^2
103041 + (x^2/4) = 190693.25
x^2/4 = 87552.25
x^2 = 350209
x ≈ √350209 ≈ 591.7
Therefore, the length of the edge of the square base, rounded to the nearest tenth, is approximately 591.7 feet.
To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the slant height of the pyramid (436.5 feet) represents the hypotenuse, and the height of the pyramid (321 feet) represents one of the sides of the right triangle.
We can solve for the other side, which represents half the length of the square base:
Let's call the unknown side length x.
Using the Pythagorean theorem: x^2 + 321^2 = 436.5^2
Simplifying the equation:
x^2 + 103041 = 190642.25
Now, isolate x^2 by subtracting 103041 from both sides:
x^2 = 190642.25 - 103041
x^2 = 87601.25
Finally, take the square root of both sides to find x:
x = √87601.25
Using a calculator, we find that x is approximately 296.1 feet.
Since the length of the edge of the square base is twice the value of x, we can multiply x by 2 to find the approximate length of the edge:
2 * 296.1 = 592.2
Therefore, to the nearest 10th, the length of the edge of the square base of the pyramid is 592.2 feet.
To find the length of the edge of the square base, we can use the Pythagorean theorem.
The Pythagorean theorem states that for a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
Let's denote the length of the edge of the square base as "x". We can form a right triangle with one of the edges of the square base as the base of the triangle, the height of the pyramid as the height of the triangle, and the slant height as the hypotenuse of the triangle.
Using the Pythagorean theorem, we have:
x^2 + (321 ft)^2 = (436.5 ft)^2
Now we can solve for x:
x^2 = (436.5 ft)^2 - (321 ft)^2
x^2 = 190350.25 ft^2 - 103041 ft^2
x^2 = 87309.25 ft^2
Taking the square root of both sides, we get:
x = sqrt(87309.25 ft^2)
x ≈ 295.4 ft
Therefore, the length of the edge of the square base is approximately 295.4 feet (rounded to the nearest 10th).