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Carpenters don't refer to the angle of a roof, such as 30º or 45º, but to the pitch of the roof, which is just the ratio of vertical to horizontal measurements. I say this because it's quite an important distinction. Angles are pretty hard to measure, but pitch is simple. An average and easy pitch to work with is a 5-12. The 5 refers to the rise of the roof and the 12 refers to the run of the roof. With the steel square (framing square) we can use these numbers directly without having to compute angles.
In your example of a 6' span or a 3' run (half the span) we could use a 2x4 for the rafters and a 1x6 for the ridge board. Refer to my article on the Steel Square for some background information. For a 5-12 pitch take your framing square and with the 5 on the tongue and the 12 on the body with the heel of the square below the rafter, scribe along the tongue to give the plumb cut. From this point along the top of the rafter, measure 3'-3" and put another plumb cut at this mark.
Now measure back up the rafter 3/8", which is half the thickness of the ridge board. On the face of the rafter, square off a line from this last measure. This is the outside wall line.
For a tree house of this size a 6" overhang should be enough. So come down from this outside wall line 6 1/2" and scribe another plumb line. Scribe another line the thickness of your rafter trim, usually 1 1/2", parallel to this plumb line to shorten the rafter. Now go back to the wall line and scribe the bird's mouth and cut it out. This is the pattern for your rafters. Try two out first before you cut the rest.
One other thing when laying out rafters or joists or beams, always have the crown of the board up so it will straighten out with the weight of the roof.
Good Luck.
