Compound Angle Help

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Uzzy

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I am hoping someone on here can help me, I am trying to build a sloping pyramid ( Sort Of ) only about 3" of one. It is to sit a cake board on. My timber has a 15 degree angle on the base to make the slope but I am confounded to the corner angles. I have watched a couple of you tube videos for coving where it is cut at an angle whilst being at an angle itself. Would this work and at what angle should I set the saw, do I need to flip each piece as I do not have a lot of material to practice with. :)
 
I've just had supper with a glass of very strong ale so find myself incapable of clear calculation. Should have read the label, Robinsons Old Tom, 8.5%.

Why not start empirically (trial by bodge) using cardboard and sellotape to make a life sized model a la Blue Peter, then you can sit back and contemplate the joint angles. I guess it's 4 identical equilateral triangles truncated so it's flat on top not pointy, and I suspect the angle where they meet one another is 90 degrees so the mitre is 45 degrees on each edge. I think they would meet the ground at 60 degrees so would need a 30 degree mitre.

Hopefully someone with a fully engaged mind will be along soon. Off for a lie down.
 
If your pyramid parts have a base edge cut at 15º this means the sides form an angle (lean inwards from the base line) at 75º. By saying pyramid I assume you're talking of a four sided structure.

Therefore the first number you require is 93.8º for the dihedral angle which means to mitre the four meeting corners you divide the dihedral angle by 2 = 46.9º. Cut the long rising edges at this, i.e., 46.9º from the outer face of the pyramid face board to the inner face of the board.

The other angle you need is the mitre angle which is 75.5º. This is the angle required between the bottom edge of each pyramid piece and each edge rising from that bottom edge.

Note that for all of the above given angles if you can cut them to within half a degree accuracy you'll be doing pretty well, e.g., don't get too upset if your attempted 75.5º cut given just above comes out anywhere between 75º and 76º.

If your base, presumably with a cut off top to carry the cake stand, has either more or less sides than four it's not a top sawn off square pyramid type structure (frustum) but some other form of polyhedron, e.g., triangular frustum, hexagonal frustum, and so on. Slainte.
 
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If it is 76mm thick timber and set back 15 degrees from the vertical the set back on the straights will be

76 Tan 15 = 20.36mm

If the truncated cone cake board is square or a rectangle the higher corner will be in 20.4 from both face.

from corner square root of 2 times 20.36 squared = 28.80mm

Angle of slope at the corner

tan angle = 28.8/76
Angle 20.75 degrees

Not sure why you want to know this angle. assuming I have understood the question. Won't you cut the straights and the angle of the corner will be what it is!
 
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