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.
How many miles long is the height of the square pyramid the slant is 61mi and the base is 11mi? The height is about?
1 answer