How many miles long is the height of the square pyramid the slant is 61mi and the base is 11mi? The height is about?
To find the height of a square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid is given as 61mi, and one side of the base is given as 11mi.
We can consider the slant height as the hypotenuse of a right triangle, with one leg being the height of the pyramid and the other leg equal to half the length of one side of the base.
Using the Pythagorean theorem:
height^2 + (1/2 * side of base)^2 = slant height^2.
Let's substitute the given values into this equation:
height^2 + (1/2 * 11mi)^2 = 61mi^2.
Simplifying:
height^2 + (1/2)^2 * 11mi^2 = 61mi^2.
height^2 + (1/4) * 121mi^2 = 61mi^2.
height^2 + 30.25mi^2 = 61mi^2.
height^2 = 61mi^2 - 30.25mi^2.
height^2 = 30.75mi^2.
Taking the square root of both sides:
height ≈ √30.75 mi^2.
height ≈ 5.53 mi (rounded to two decimal places).
Therefore, the height of the square pyramid is approximately 5.53 miles.
To find the height of the square pyramid given the slant height and base length, we can use the Pythagorean Theorem. In a right triangle formed by the height, slant height, and half of the base, the height is the missing side.
Let's denote the height as "h," the slant height as "l," and the half of the base as "b."
We know that the slant height is 61 mi, and the base is 11 mi.
Using the Pythagorean Theorem:
h^2 + b^2 = l^2
Substituting the known values:
h^2 + (11/2)^2 = 61^2
h^2 + 121/4 = 3721
h^2 = 3721 - 121/4
h^2 = 3600
h = √3600
h = 60
Therefore, the height of the square pyramid is approximately 60 miles.
To find the height of a square pyramid, we need to use the Pythagorean theorem. The slant height (l) acts as the hypotenuse of a right-angle triangle, while the height (h) and half the base length (b/2) form the other two sides.
We are given the slant height (l = 61 mi) and the base length (b = 11 mi). Therefore, we can substitute these values into the Pythagorean theorem:
l^2 = (b/2)^2 + h^2
Substituting the known values into the equation:
(61 mi)^2 = (11 mi / 2)^2 + h^2
Now, we can calculate the height:
(61 mi)^2 - (11 mi / 2)^2 = h^2
(3721 mi^2) - (121 mi^2 / 4) = h^2
(3721 mi^2 - 121 mi^2 / 4) = h^2
(3721 mi^2 - 30.25 mi^2) = h^2
3690.75 mi^2 = h^2
To find the height, we can take the square root of both sides of the equation:
√(3690.75 mi^2) = √h^2
h ≈ √3690.75 mi
Using a calculator, we find that h ≈ 60.78 mi.
Therefore, the height of the square pyramid is approximately 60.78 miles.