Question
How many miles long is the height of the square pyramid the slant is 61mi and the base is 11mi? The slant height is about?
Answers
GPT 3.5
To find the height of the square pyramid, we can use the Pythagorean theorem.
The slant height represents the hypotenuse of a right triangle formed by the height, base, and slant height.
Let the height of the pyramid be represented by "h".
Using the Pythagorean theorem, we have:
h^2 + (11/2)^2 = 61^2
h^2 + 121/4 = 3721
4h^2 + 121 = 14884
4h^2 = 14884 - 121
4h^2 = 14763
h^2 = 14763/4
h ≈ √(14763/4)
h ≈ √3690.75
h ≈ 60.82
Therefore, the height of the square pyramid is approximately 60.82 miles long.
The slant height is given as 61 miles.
The slant height represents the hypotenuse of a right triangle formed by the height, base, and slant height.
Let the height of the pyramid be represented by "h".
Using the Pythagorean theorem, we have:
h^2 + (11/2)^2 = 61^2
h^2 + 121/4 = 3721
4h^2 + 121 = 14884
4h^2 = 14884 - 121
4h^2 = 14763
h^2 = 14763/4
h ≈ √(14763/4)
h ≈ √3690.75
h ≈ 60.82
Therefore, the height of the square pyramid is approximately 60.82 miles long.
The slant height is given as 61 miles.