The Pythagorean Theorem in Three Dimensions Practice
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Question
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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.
thx!
@Bretothecat
all answers
WRONG I GOT A 0!!!
here are the answers to the questions<3
1.40
2.31.5
3.50
4.24
5.34.5
<3
To find the length of the edge of the square base, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Where a and b are the two sides of the triangle formed by the height, slant height, and the edge of the base, and c is the hypotenuse (slant height).
In this case, one side of the triangle is the height (321 ft) and the other side is the length of the edge of the square base (l ft). The hypotenuse is the slant height (436.5 ft).
We can plug these values into the Pythagorean theorem:
321^2 + l^2 = 436.5^2
103041 + l^2 = 190522.25
l^2 = 190522.25 - 103041
l^2 = 87481.25
l = √87481.25
l ≈ 295.5 ft
So, the length of the edge of the square base is approximately 295.5 ft.
To solve this problem, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle formed by the slant height (436.5 ft), the height (321 ft), and the length of one of the edges of the square base (l).
Using the Pythagorean Theorem, we can write:
l^2 = 436.5^2 - 321^2
Calculating this, we get:
l^2 = 190512.25 - 103041
l^2 = 87471.25
To find the length of the edge of the square base (l), we can take the square root of both sides:
l = √87471.25
Rounding to the nearest tenth, we get:
l ≈ 295.6 ft.
So, the length of the edge of the square base is approximately 295.6 ft.
ALL THE ANSWERS FOR PRACTICE ILL PUT THE QUICK CHECK AS SOON AS I GET ALL THE RIGHT ANSWERS FOR THAT TOO:
1. 12
2. 40.3
3. 23
4. 591.6
5. 132.6
>_<
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 (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can view the triangle formed by one of the edges of the square base, the height, and the slant height. The length of the edge of the square base is one of the legs of this right triangle, the height is the other leg, and the slant height is the hypotenuse.
Let's label the length of the edge of the square base as "l". According to the Pythagorean theorem, we have the equation: l^2 + 321^2 = 436.5^2.
To solve for "l", we need to isolate it on one side of the equation. Start by subtracting 321^2 from both sides: l^2 = 436.5^2 - 321^2.
Next, calculate the values on the right side of the equation: l^2 = 189922.25 - 103041.
Finally, find the square root of both sides to solve for "l": l ≈ √86881.25 ≈ 294.8.
Rounding the answer to the nearest tenth, the length of the edge of the square base is approximately 294.8 feet.
CREDIT GOES TO @mitskilover
1. 15.0
2. 59.5
3. 8.8
4. 9.1
5. 92.9
BYE :3 have a nice night.......