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i am attaching a lean-to top to an outdoor building. The place we put the ledger board is at an angle. It's a barn shaped building. We don't know how to figure the angle.
 

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uva uvam vivendo variafit
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Put a framing square on the rafter and use a level to make sure the either the vertical leg of the square is plumb or the horizontal leg is level. Then measure from the corner of the square vertically (the rise) and horizontally (the run) to the rafter. Try to maximize the dimensions that you are measuring by pulling the square away from the rafter - this will give you a more accurate reading. The angle measured from the horizon up to the rafter will be the arctangent of rise divided by the run. If you want to set your miter box the angle would 90 degrees minus the angle that you just calculated.
 

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You can also hold the rafter stock against the side on the ledger and the beam on the other side as it's going to sit and just scribe it. You can scribe the seat cut too. You can frame your lean-to without ever even having to know what the angle is.
 
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