If you would like to frame with angles, this is the long hand method.
a2+b2=c2
A= 54-43
B= depth of coop
C=Length of roof section from front to back.
The cut on the top of the post is Parrallel with the hypotenuse or Leg C.
That angle can be found by the following:
A = difference in height from between front and back of coop. We'll call this the short leg = 9"
B= Depth of coop We'll call this the long leg
C=the roof or hypotenuse.
The angle where the roof touches the front wall is a
The angle where the roof touches the rear wall is b
If you imagine you coop is built as a square with a triangle on top creating the roof angle, this is the triangle we are figuring the angles for.
The value of angle a = sin (opposite(A)/hypotenuse(C)).
If your coop were 48" deep, this is what we would be looking at...
A=9", B=48"
We are looking for C, a, b.
C=the square root of (9(squared) + 48(squared) = 48.84"
a=Sin(9/48.84)=10.62*
b = 90 - 10.62* or 79.38
The value of angle b= angle a - 90*. The angles inside a right triangle must = 180*.
Now we have all the angles of your roof triangle. The angle of the cut on the post(s), will be the value of angle (a) swept up from horizontal, or the value of angle (b) swept up from vertical. It is the same for both posts.
You can also use rise run.
Rise is 9" run is 48" so 9/48 or 4.5/24 or 2.25/12, pretty close to 2/12 pitch. If you have not cut anything yet, use the 2/12 value to frame your end walls. In essence, let the roof slope dictate the wall heights. It should be less than an inch difference.
Always use math to frame a roof and walls if you want them to be square and true. It ALWAYS works. Just make sure to take your time, always measure from the same point of reference (i.e outside of timbers or inside of timbers), and double check your measurements. After you have calculated your angles, and have your boards marked, clamp a straight edge on it and make sure it looks right. When it looks good, frame to your marks and everything will fall right in line, because it has to. Math does not lie.
The only place I run things long is rafters, and that is because I like to make sure the over hang planned on is enough, or possibly to much.
And you said you would never use that algebra crap in the real world!!! HA!
HAPPY FRAMMING!!!!