(11-15-2010, 11:08 PM)Bring4th_GLB Wrote: (11-12-2010, 07:21 AM)unity100 Wrote: well, just take the diagonal that runs from one corner of the base of the pyramid rectangle to the another as the bottom side of the 2d triangle you need, and cut the wood to form 60 degree angles with them.

Really? I mean, seriously? "Cut the wood to form sixty degree angles with them"?

Unity100, jeez. Did you read my post? : )

I appreciate your attempt to be helpful but should you endeavor another try, I would encourage a review of the fifth sentence of my previous post in this thread.

GLB

for a 60 degree top angle pyramid, it means you are constructing an isosceles triangle when you look at its cross section from the side.

that means, the sides you see in the cross section will constitute equal lengths, because all the degrees of the triangle you see will be 60.

this means, also the width of the pyramid, and one side of the base, and, the line that runs from the middle of the pyramid's side, to the apex, will be equal in length. because the cross section triangle needs to be isosceles.

this means, when you look at the surface that will end up in a side of the pyramid, there will be x length, at the bottom of the triangle you see on the surface, and, there will also be x length running from the middle at the bottom of that triangle, to the apex.

so then, we now know the height of the triangle that forms on the surface. its x. we also know that, that height starts from the middle of the one side pyramid's base and goes to the top. that means, the height also divides that side of the pyramid, from the middle. the bottom side of the pyramid had length x. that means half of it will constitute length x/2.

now, when looking at the surface we see 2 triangles that are created on the surface with the height we ran from middle of the side of the pyramid at bottom to the apex : there are 2 equal right triangles.

you know the length of the 2 sides of these triangles : one side is x length (the height which runs from middle of the side of the pyramid to the apex on surface), the other side is x/2 (the side of the pyramid divided into two at the bottom).

that leaves only Pythagorean theorem necessary to get the result :

the length of the long side of those right triangles will be the square root of the summation of squares of x, and x/2.

namely square root of (( (x)^2) + ((x/2)^2).

http://en.wikipedia.org/wiki/Hypotenuse