whats 2*90
9 answers
2 * 90 is 180.
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.
The Pyramid in Memphis (officially known as the Great American Pyramid) was originally built as a sports arena and is now a Bass Pro Shops mega store and hotel. It is indeed shaped like a pyramid, with a square base and four triangular sides that meet at a point.
To find the length of the edge of the square base, you can use the Pythagorean theorem on one of the triangular faces. This triangular face is an isosceles triangle since two of its sides are equal (the slant heights), and the base would be one side of the square.
The triangular face can be split into two right triangles, each having:
- The slant height of 436.5 ft as the hypotenuse.
- Half the length of the base edge (let's call this 'b/2') as one leg.
- The height of the pyramid, 321 ft as another leg.
Using the Pythagorean theorem, we can express the relationship between the sides of a right triangle as:
(hypotenuse)^2 = (leg1)^2 + (leg2)^2
And here, we'll substitute the known values:
(436.5 ft)^2 = (321 ft)^2 + (b/2)^2
Now we can solve for b/2:
1909922.25 = 103041 + (b/2)^2
1909922.25 - 103041 = (b/2)^2
1805881.25 = (b/2)^2
Now, take the square root:
sqrt(1805881.25) ≈ 1343.822
So half the base (b/2) is approximately 1343.8 ft, and the full edge length of the base (b) would be twice this, so:
b = 2 * 1343.8
b ≈ 2687.6
Therefore, the edge of the square base is approximately 2687.6 ft. Since we want to round it to the nearest tenth, it becomes:
2687.6 ft (rounded to the nearest tenth)
To find the length of the edge of the square base, you can use the Pythagorean theorem on one of the triangular faces. This triangular face is an isosceles triangle since two of its sides are equal (the slant heights), and the base would be one side of the square.
The triangular face can be split into two right triangles, each having:
- The slant height of 436.5 ft as the hypotenuse.
- Half the length of the base edge (let's call this 'b/2') as one leg.
- The height of the pyramid, 321 ft as another leg.
Using the Pythagorean theorem, we can express the relationship between the sides of a right triangle as:
(hypotenuse)^2 = (leg1)^2 + (leg2)^2
And here, we'll substitute the known values:
(436.5 ft)^2 = (321 ft)^2 + (b/2)^2
Now we can solve for b/2:
1909922.25 = 103041 + (b/2)^2
1909922.25 - 103041 = (b/2)^2
1805881.25 = (b/2)^2
Now, take the square root:
sqrt(1805881.25) ≈ 1343.822
So half the base (b/2) is approximately 1343.8 ft, and the full edge length of the base (b) would be twice this, so:
b = 2 * 1343.8
b ≈ 2687.6
Therefore, the edge of the square base is approximately 2687.6 ft. Since we want to round it to the nearest tenth, it becomes:
2687.6 ft (rounded to the nearest tenth)
thats wrong
My apologies for the mistake in my previous calculation. Let's correct that.
We have the slant height (l) of the pyramid as 436.5 ft and the height (h) of the pyramid as 321 ft. Since the Pyramid is in the shape of a regular square pyramid, if we cut it in half from the apex (top) to the center of the base, we will have a right triangle where the slant height is the hypotenuse, the height of the pyramid is one leg, and half the base (b/2) is the other leg.
We can use the Pythagorean theorem to solve for b/2:
l^2 = h^2 + (b/2)^2
Plug in the known values:
436.5^2 = 321^2 + (b/2)^2
Now let's solve for (b/2)^2:
190522.25 = 103041 + (b/2)^2
190522.25 - 103041 = (b/2)^2
87581.25 = (b/2)^2
Now solve for b/2 by taking the square root:
b/2 = sqrt(87581.25)
b/2 ≈ 295.94
Now we can find the full length of the base (b) by doubling this value:
b = 2 * 295.94
b ≈ 591.88
So, the length of the edge of the square base is approximately 591.88 ft. Rounding to the nearest tenth, the edge length is:
591.9 ft
We have the slant height (l) of the pyramid as 436.5 ft and the height (h) of the pyramid as 321 ft. Since the Pyramid is in the shape of a regular square pyramid, if we cut it in half from the apex (top) to the center of the base, we will have a right triangle where the slant height is the hypotenuse, the height of the pyramid is one leg, and half the base (b/2) is the other leg.
We can use the Pythagorean theorem to solve for b/2:
l^2 = h^2 + (b/2)^2
Plug in the known values:
436.5^2 = 321^2 + (b/2)^2
Now let's solve for (b/2)^2:
190522.25 = 103041 + (b/2)^2
190522.25 - 103041 = (b/2)^2
87581.25 = (b/2)^2
Now solve for b/2 by taking the square root:
b/2 = sqrt(87581.25)
b/2 ≈ 295.94
Now we can find the full length of the base (b) by doubling this value:
b = 2 * 295.94
b ≈ 591.88
So, the length of the edge of the square base is approximately 591.88 ft. Rounding to the nearest tenth, the edge length is:
591.9 ft
thats wrong again
I apologize for the oversight. Let's correct the calculation.
We need to find the length of the base edge ('b') of the Pyramid using the Pythagorean theorem. The slant height ('l') is the hypotenuse of the right triangle formed when we split the face of the pyramid down the middle. The height ('h') of the Pyramid is one leg of the triangle, and half the base edge ('b/2') is the other leg.
Using the Pythagorean theorem:
\( l^2 = h^2 + (b/2)^2 \)
Given values:
\( l = 436.5\;ft \)
\( h = 321\;ft \)
We can plug these values into the Pythagorean theorem to solve for \( b/2 \):
\( (436.5)^2 = (321)^2 + (b/2)^2 \)
\( 190522.25 = 103041 + \frac{b^2}{4} \)
Solving for \( b^2 \):
\( 190522.25 - 103041 = \frac{b^2}{4} \)
\( 87481.25 = \frac{b^2}{4} \)
Multiply both sides by 4 to solve for \( b^2 \):
\( 4 \times 87481.25 = b^2 \)
\( 349925 = b^2 \)
Now take the square root to solve for \( b \):
\( b = \sqrt{349925} \)
\( b \approx 591.5 \)
So the length of each edge of the base is approximately 591.5 feet. However, because the decimal place is already at the nearest tenth, you do not need to round it further. The edge of the square base is approximately 591.5 feet.
We need to find the length of the base edge ('b') of the Pyramid using the Pythagorean theorem. The slant height ('l') is the hypotenuse of the right triangle formed when we split the face of the pyramid down the middle. The height ('h') of the Pyramid is one leg of the triangle, and half the base edge ('b/2') is the other leg.
Using the Pythagorean theorem:
\( l^2 = h^2 + (b/2)^2 \)
Given values:
\( l = 436.5\;ft \)
\( h = 321\;ft \)
We can plug these values into the Pythagorean theorem to solve for \( b/2 \):
\( (436.5)^2 = (321)^2 + (b/2)^2 \)
\( 190522.25 = 103041 + \frac{b^2}{4} \)
Solving for \( b^2 \):
\( 190522.25 - 103041 = \frac{b^2}{4} \)
\( 87481.25 = \frac{b^2}{4} \)
Multiply both sides by 4 to solve for \( b^2 \):
\( 4 \times 87481.25 = b^2 \)
\( 349925 = b^2 \)
Now take the square root to solve for \( b \):
\( b = \sqrt{349925} \)
\( b \approx 591.5 \)
So the length of each edge of the base is approximately 591.5 feet. However, because the decimal place is already at the nearest tenth, you do not need to round it further. The edge of the square base is approximately 591.5 feet.
thats not the answer whats the real answer
My apologies for the confusion earlier. Let's go through the calculation once more.
Given:
- Slant height (l) = 436.5 ft
- Height (h) = 321 ft
We'll use the Pythagorean theorem for the right triangle that's formed by the height of the pyramid, half of the base length, and the slant height.
Pythagorean theorem formula:
\( l^2 = h^2 + (b/2)^2 \)
We have to solve for \( b \) (full length of the base), and we'll start by solving for \( b/2 \) (half of the length of the base).
First, let's insert the values we have:
\( (436.5)^2 = (321)^2 + (b/2)^2 \)
Now, calculate the squares:
\( 190522.25 = 103041 + (b/2)^2 \)
Next, subtract \( 103041 \) from both sides to isolate \( (b/2)^2 \):
\( (b/2)^2 = 190522.25 - 103041 \)
\( (b/2)^2 = 87481.25 \)
Now, take the square root of both sides to solve for \( b/2 \):
\( b/2 = \sqrt{87481.25} \)
\( b/2 ≈ 295.77 \)
To find the full length of the base (b), we multiply this result by 2:
\( b = 2 * 295.77 \)
\( b ≈ 591.54 \)
Based on this calculation, the length of the edge of the square base is approximately 591.54 feet. When rounded to the nearest tenth, it is 591.5 feet.
Given:
- Slant height (l) = 436.5 ft
- Height (h) = 321 ft
We'll use the Pythagorean theorem for the right triangle that's formed by the height of the pyramid, half of the base length, and the slant height.
Pythagorean theorem formula:
\( l^2 = h^2 + (b/2)^2 \)
We have to solve for \( b \) (full length of the base), and we'll start by solving for \( b/2 \) (half of the length of the base).
First, let's insert the values we have:
\( (436.5)^2 = (321)^2 + (b/2)^2 \)
Now, calculate the squares:
\( 190522.25 = 103041 + (b/2)^2 \)
Next, subtract \( 103041 \) from both sides to isolate \( (b/2)^2 \):
\( (b/2)^2 = 190522.25 - 103041 \)
\( (b/2)^2 = 87481.25 \)
Now, take the square root of both sides to solve for \( b/2 \):
\( b/2 = \sqrt{87481.25} \)
\( b/2 ≈ 295.77 \)
To find the full length of the base (b), we multiply this result by 2:
\( b = 2 * 295.77 \)
\( b ≈ 591.54 \)
Based on this calculation, the length of the edge of the square base is approximately 591.54 feet. When rounded to the nearest tenth, it is 591.5 feet.