I'm going to install a lean to shelter onto the house with timber plate bolted to the house and the other onto timber posts. Plates will be 6x2 and rafters 4x2. How do I best calculate the pitch? I understand how to do the calculations etc, but I'm getting confused because the top end of the rafter will be flush with the top of wall plate where bottom will be birds mouth. So if measuring from outside of bottom plate where do I take measurement to on the top wall plate on the house? Cant be as simple as going 3" down on the plate if birds mouth is 1" in at the bottom as the rafter will be at an angle so distance will be different? Hope someone is able to help! Thanks in advance.
Offer a timber up to sit over the two plates with an angle cut on the top end just to ensure that the rafter can sit on top of the bearer/ledger/wall plate without the bottom edge pushing it off. Mark a plumb line anywhere on the rafter then cut the top of the rafter plumb cut at that angle. Divide the width of your rafter into thirds, then mark a line all the way down the rafter two thirds from the top. Then doing the cheats way rather than geometry or maths, measure from the top of the ledger plate to the outside edge of the wall plate, then measure from your top of the plumb cut on your rafter down to the required distance and make the mark on the line you drew earlier. Use your plumb cut angle to send the line through the intersection point you've just marked, then using a square come 90 degrees off that and mark a line, that triangle is to be cut out, and is your birdsmouth cut.