Expert: Dan Griffin - 3/20/2010

Question
I'm building a sun deck off the side of my cottage with the header lagged to the wall studs of the cottage at a 1st. height and the front wall being 8ft.high for a 2ft. slope over 1st.What will the angle on the header be and the angle for the bird mouth on the other end of a 2x6 roof joyce.I will have a 1ft. over hang for sofet and face boards. Thank You.

Answer
Scott, it is very hard to follow your question.

A few basic terms
a deck is usually something you walk or sit on
a sun shade is a roof-like:structure
a joist is a horizontal member that you walk on or carries a ceiling
a rafter is a slanted member that carries a roof
a soffit is the horizontal under side of an eave overhang
a fascia is the vertical face of an eave overhang
I think that your 1st means the 1st floor level
a header carries loads over openings in walls
a birds mouth sits on an outside plate, often a header
a ledger band is mounted to studs or similar to carry one end of rafters or joists

I think you are telling me that you are creating a single shed roof (a sun shade ????) from the side of your house.  You intend to install a ledger band on the side of the house to carry the top of the rafters.  The rafters will extend some unknown amount away from the house to sit on something, probably a stud wall or perhaps just a header on columns.  I guess the shade is over a patio or deck or something similar.  You are asking the angles of the pitched rafter cuts.

This is known as the rise and run of a rafter.  I think you are telling me that it will be 2' higher at the top than at the outside wall with a one foot overhang.  You must know the the horizontal distance that the rafter must travel and the amount it will rise.  The length of the rafter and the angles involved will be different for any changes in either rise or run.  Swanson speed squares, framing squares, and many carpentry terms deal with the slope of the rafter, often labeled the fall per foot.

Let's assume that the rise is 40" and that the outside of the outside wall is 10' away from the house.  Then the slope of the roof will be "4 in 12" (40 divided by 10 = 4" in each of ten feet)  Once you know the slope of the roof, the Swanson speed square is a very simple way to draw the angles.  Another method would be to use a framing square and set the number 4 of the tongue and the number 12 of the blade on one edge of the 2x6 rafter and draw the line on the tongue, same thing on the bottom drawing the line of the blade give the birds mouth.  The angles can be solved with trigonmetry using the run as the base and rise as the perpendicular, thus 40 divided by 120 = the tangent of the acute angle which is 18.3 degrees.

This site has several well done pictures that may help you:
http://www.builderbill-diy-help.com/rafter-cuts.html#toc1

I hope this helped and if you have further questions let me know.