The Great Pyramid of Giza in Egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. Find the height of the pyramid. Round the answer to the nearest tenth. po
just answer the question
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 (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the pyramid represents one of the legs of a right triangle, the slant height represents the hypotenuse, and the base of the pyramid represents the other leg.
Let's label the sides of the triangle:
- Base of the pyramid = 230.5 m
- Height of the pyramid = h (what we want to find)
- Slant height = 180.2 m
Using the Pythagorean Theorem, we have:
(h)^2 + (230.5)^2 = (180.2)^2
Simplifying the equation:
h^2 + 53130.25 = 32472.04
Subtracting 53130.25 from both sides:
h^2 = 32472.04 - 53130.25
h^2 = -20658.21
Since we cannot take the square root of a negative number, it means we made a mistake or there is an inconsistency in the given information.
Please check the given values for accuracy.
I apologize for the confusion. Given the information, let's assume that it is accurate.
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 (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the pyramid represents one of the legs of a right triangle, the slant height represents the hypotenuse, and the base of the pyramid represents the other leg.
Let's label the sides of the triangle:
- Base of the pyramid = 230.5 m
- Height of the pyramid = h (what we want to find)
- Slant height = 180.2 m
Using the Pythagorean Theorem, we have:
(h)^2 + (230.5)^2 = (180.2)^2
Simplifying the equation:
h^2 + 53130.25 = 32544.04
Subtracting 53130.25 from both sides:
h^2 = 32544.04 - 53130.25
h^2 = -20586.21
Since we cannot take the square root of a negative number, it means there is an inconsistency in the given information or I made a mistake.
Please check the given values for accuracy.
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 hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the height of the pyramid is the side opposite the right angle, the slant height is the hypotenuse, and the length of the base is one of the other two sides.
Let's label the height as 'h', the slant height as 'l', and the length of the base as 'b'.
According to the Pythagorean theorem:
h^2 + (b/2)^2 = l^2
Substituting the given values:
h^2 + (230.5/2)^2 = 180.2^2
Simplifying:
h^2 + 26452.25 = 32544.04
h^2 = 32544.04 - 26452.25
h^2 = 6091.79
To find the value of h, we take the square root of both sides:
h = √6091.79
Using a calculator, we find that h is approximately 78.1 (rounded to the nearest tenth).
Therefore, the height of the pyramid is approximately 78.1 meters.