Use the image to answer the question.
A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
(1 point)
ft.
To find the length of the edge of the square base, we can use the Pythagorean theorem. The slant height, height, and one side of the base form a right triangle.
Let's label the length of the edge of the square base as "l".
Using the Pythagorean theorem, we have:
l^2 = (436.5)^2 - (321)^2
l^2 = 190.5225 - 103041
l^2 = 103230.4775
Taking the square root of both sides to solve for l:
l = √103230.4775
l ≈ 321.1
Therefore, the length of the edge of the square base is approximately 321.1 ft.
To find the length of the edge of the square base, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height (the hypotenuse) represents the diagonal of one of the square base's sides, and the height represents one of the legs of the right-angled triangle.
Using the Pythagorean Theorem, we can set up the equation:
l^2 + h^2 = slant height^2
l^2 + 321^2 = 436.5^2
Simplifying the equation:
l^2 + 103041 = 191194.25
l^2 = 88153.25
Taking the square root of both sides to solve for l:
l = √88153.25
l ≈ 296.9 ft.
Therefore, the length of the edge of the square base is approximately 296.9 feet.
To find the length of the edge of the square base, we can use the Pythagorean theorem. The formula for the Pythagorean theorem is:
a^2 + b^2 = c^2
In this case, the height of the pyramid (321 ft) is the vertical side (a), and the slant height (436.5 ft) is the hypotenuse (c). We need to find the length of the base edge (b).
We can rearrange the formula to solve for b:
b^2 = c^2 - a^2
Now we can substitute the known values into the equation:
b^2 = (436.5 ft)^2 - (321 ft)^2
Simplifying:
b^2 = 190,522.25 ft^2 - 103,041 ft^2
b^2 = 87,481.25 ft^2
To find b, we need to take the square root of both sides:
b = √(87,481.25 ft^2)
Using a calculator, we find:
b ≈ 295.6 ft
Therefore, the length of the edge of the square base is approximately 295.6 ft. Rounded to the nearest tenth, the answer is 295.6 ft.