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.(1 point)
Using the Pythagorean theorem, we can find the height of the pyramid.
The slant height, base, and height form a right-angled triangle.
The square of the slant height is equal to the sum of the squares of the base and the height.
Therefore, we can write the equation as follows:
180.2^2 = (230.5^2) + height^2
32,496.04 = 53,122.25 + height^2
height^2 = 32,496.04 - 53,122.25
height^2 = -20,626.21
Since the height of a pyramid cannot be negative, we reject this solution.
Therefore, there is no real height for the pyramid with the given measurements.
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 perpendicular distance from the apex (top) to the center of the square base, which forms a right triangle with the slant height (180.2 m) as the hypotenuse and half of the base length (230.5 m / 2 = 115.25 m) as one of the legs.
So, we can use the Pythagorean theorem as follows:
height^2 + (base/2)^2 = slant height^2
Let's substitute the given values into the formula:
height^2 + (115.25 m)^2 = (180.2 m)^2
Next, we solve for the height by isolating it on one side of the equation:
height^2 = (180.2 m)^2 - (115.25 m)^2
height^2 = 32544.04 m^2 - 13286.5625 m^2
height^2 = 19257.4775 m^2
Now, find the square root of both sides of the equation to solve for the height:
height ≈ √(19257.4775 m^2)
height ≈ 138.7 m (rounded to the nearest tenth)
Therefore, the height of the Great Pyramid of Giza is approximately 138.7 meters.
To find the height of the pyramid, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides (in this case, the height and half the base).
So, we can write the equation as:
(Height)^2 + (Base/2)^2 = Slant Height^2
Let's substitute the given values into the equation:
(Height)^2 + (230.5/2)^2 = 180.2^2
Simplifying this equation:
(Height)^2 + 26570.25 = 32544.04
Next, we can isolate (Height)^2 by subtracting 26570.25 from both sides:
(Height)^2 = 32544.04 - 26570.25
(Height)^2 = 5973.79
To find the height, we take the square root of both sides:
Height = sqrt(5973.79)
Using a calculator, the height is approximately 77.3 meters when rounded to the nearest tenth.