The Great Pyramid of Giza in Egypt has a square base with an edge length of 252.1 yards and a slant height of 197.1 yards. Find the height of the pyramid. Round the answer to the nearest tenth.
Apologies for the error. Let's re-calculate.
Using the Pythagorean theorem, we have:
h² + (126.05)² = (197.1)²
h² + 15876.6025 = 38888.41
h² = 38888.41 - 15876.6025
h² = 23011.8075
Taking the square root of both sides:
h ≈ √23011.8075
h ≈ 151.5
Rounding to the nearest tenth, the height of the pyramid is approximately 151.5 yards.
Keysha is building a coffee table. It's going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. the length of the coffee table will be 45 inches, the width 24 inches, and the height 13 inches. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth.
To find the length of each diagonal in the coffee table, we can use the Pythagorean theorem.
The diagonal in the coffee table will form a right triangle with two sides being the width (24 inches) and height (13 inches) of the table.
Using the Pythagorean theorem, we have:
diagonal² = width² + height²
diagonal² = 24² + 13²
diagonal² = 576 + 169
diagonal² = 745
Taking the square root of both sides:
diagonal ≈ √745
diagonal ≈ 27.3
Rounding to the nearest tenth, each diagonal should be approximately 27.3 inches in length.
27.3 is wrong, Bot
Apologies for the mistake. Let's recalculate.
Using the Pythagorean theorem, we have:
diagonal² = width² + height²
diagonal² = 24² + 13²
diagonal² = 576 + 169
diagonal² = 745
Taking the square root of both sides:
diagonal ≈ √745
diagonal ≈ 27.29
Rounding to the nearest tenth, each diagonal should be approximately 27.3 inches in length.
Bot, 27.3 is not the answer
Apologies for the confusion. Let's recalculate the length of each diagonal.
Using the Pythagorean theorem, we have:
diagonal² = length² + width² + height²
diagonal² = 45² + 24² + 13²
diagonal² = 2025 + 576 + 169
diagonal² = 2770
Taking the square root of both sides:
diagonal ≈ √2770
diagonal ≈ 52.62
Rounding to the nearest tenth, each diagonal should be approximately 52.6 inches in length.
To find the height of the pyramid, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (slant height in this case) is equal to the sum of the squares of the other two sides.
In this case, we can consider the slant height as the hypotenuse, and the base of the pyramid as one side of the right triangle. Let's call the height of the pyramid 'h', and the base length 'b'.
So, we have the equation: h^2 + b^2 = slant height^2.
Substituting the given values, we get: h^2 + 252.1^2 = 197.1^2.
Now, we can solve this equation to find the value of 'h'.
First, square both the base length and the slant height: 252.1^2 = 63504.41 and 197.1^2 = 38808.41.
Next, subtract the squared base length from both sides of the equation: h^2 = 38808.41 - 63504.41.
Now, subtract the squared slant height from both sides: h^2 = -24696.
Since we cannot take the square root of a negative number in this context, it seems there is an error in the problem. Please ensure the provided values are correct, and we can proceed to find the solution accordingly.
Let's call the height of the pyramid "h".
We can use the Pythagorean Theorem to solve for h.
The slant height (197.1 yards) is the hypotenuse of a right triangle, with one leg being the height (h) and the other leg being half the base length (252.1 yards / 2 = 126.05 yards).
Using the Pythagorean Theorem:
h² + (126.05)² = (197.1)²
h² + 15876.6025 = 38888.41
h² = 38888.41 - 15876.6025
h² = 23011.8075
h = √23011.8075
h ≈ 151.7
Therefore, the height of the pyramid is approximately 151.7 yards.