Angles for cutting

Trying to figure what angle to set my saw to for the corners of a counter top that is non-standard. I googled terms that I thought made sense and everything pointed to Pythagoras, which I use to find lengths of the boards to cut (which I already have done). I am trying to figure the angles of the two ends. I know I can use sample wood to guestimate, but I would like to learn the proper way. I have a counter top 6 feet wide. One end is 4 feet deep and the other is 2 feet deep. I know the wall side has two 90's which are two 45 degree cuts, but the outter side is the question. Any help is appreciated.

 

Trying to figure out where you want to cut. Show cuts on diagram.

 

If the cut you are trying to make is from the 2 foot side end to the 4 foot side end, the angle is 71.6 degrees CCW from the horizontal in your diagram (2 or 4 foot side). You get this from the right triangle not bordered in your diagram. The base is 2 feet and the height is 6 feet. The tangent of the angle is side opposite divided by side adjacent which is 6/2 in this triangle. The angle whose tangent is 3 is 71.6 degrees. Having said all this, with a piece so large, would not a guide board clamped to the counter top parallel to the corner to corner line be easier?

 

Countertop miters are always cut at a 45. Sometimes that 45 will be dogeared (squared off on the end) if one side is wider than the other, especially when backsplash is involved... there needs to be an additional backsplash piece added on in those cases.

It would have been good to have custom ordered this countertop so that all you had to do was assemble it.

 

Thanks BB for the info. What I will probably do is use a laser level to mark where the cuts should go. I have other things coming up and there were other things in the past where I wish I knew how to calculate for the cut, so I appreciate the knowledge.

 

http://i.imgur.com/fqvsNk0.jpg



Is this the cut?

 

Yes it is. There will also be support struts every 18 or 24 inches that will also need to be cut at that angle on one end. I drew lines from my laser level and on the saw it came to about 17ish degrees.