Who is asking: Teacher
Is there a formula that allows me to calculate the range of degrees that would work given the base of the pyramid (e.g. square, pentagonal, hexagonal, etc.)?
Thanks for your help.
Imagine that you draw a square on the ground and drive a peg at each of the four corners. Tie an elastic band across each of the two diagonals to form the diagram below.
This forms a "pyramid" of zero height and each of the four triangles has interior congruent angles of 45o.
Now grab the two elastic bands where they cross an lift them vertically off the ground to form a pyramid. As the height of the pyramid increases, the interior congruent angles on each side also increase. The taller the pyramid, the closer these angles are to 90o. Hence the interior congruent angles can have any value greater than 45o and less than 90o.
The same idea will work for any regular polygon as the base. Draw a line from each vertex to the center of the polygon to form triangles with the interior congruent angles having minimum possible angle measurement.Cheers,