First of all, I'm horrible with math. I'm trying to figure out the angles needed to make a box with mitred corners and angled sides. I wish I could find a photo of what I mean but I haven't seen any. I'd like about a 15 degree angle so the sides (and ends) of the box angle outwards making a larger top opening than bottom. Make sense? Clear as mud right!
Do you just want 'the answer' or do you want to know how to figure it out?
The easiest way to figure it out in a 'non-math' kind of way is to do it visually using lay-out. This is how a lot of guys do it. You know how high you want your box to be, yes? And you know basically what size you want the top or bottom of the box to be, yes? Draw at full scale a triangle that shows the shape of the side of the box. This will let you figure out how much the 15 degrees is going to affect the length of each side in one dimension. You could also just use the equation X = H tan(Θ) where X is the extension, H is the height of the box, and Θ is the angle (in this case 15 degrees). So if you want the box to be, say, 10" high then the extension = X = 10 * tan(15) = 2.68" which means the shape of each side of the box will be 2.68" longer on each end at the top vs. the bottom. The sides will need to be cut longer in height to account for the angle as well, and that is shown by Pythagoras where L = sqrt (10^2 + 2.68^2) = 10.35"
So of the box will be, say, 12" x 24" in plan view at the top, and 10" high, then you will have two trapezoidal pieces that are 12" long on the top edge, 6.64" long on the bottom edge, and 10.35" high. The other two trapezoidal pieces will be 24" on the top edge, 18.64" on the bottom edge, and 10.35" high.
The simple non-math way is to do the full-size layout of the triangle that I mentioned before, where you will have a vertical line 10" long (the height of the box) then you will use a protractor to put in a line 15 degrees away from that line. Draw a horizontal from the top of the 'height' line and you will have a right-angled triangle. Measure the long side and it will be the 10.35" number that you needed for the height of the sides, and the length of the shortest side is the 2.68" length to shorten the bottom of each end of each side. Cut your sides full-size (25" x 10.35", 12" x 10.35") then on each end of each side mark the 2.68" in, and mark a line and cut them all out. Done.
If you just want to know what that angle is that you need to cut the ends at, then you just have to do a new triangle using the 10.35" value and it shows the angle Φ = arctan(2.68 / 10.35) or 14.5 degrees.
You mean like this ?????...... I just used a compound cut calculator found on the internet and built a quickie jig/sled to make the cut. A wixey gauge really helps to nail the 1/10th deg accuracy needed to close the corners.