Well, like I said it was hard to follow.Glad you got it.But if your center line rise was 15.5 with a 36" base line, that is 23.29 degrees instead of the 22.5. Didn't mean to confuse.

if you dont wanna get confuse......whatever your size of your check elbow get size half of it..sample 30 size of your check =15 and then your distance to the throat radius add it together thats your centre line radius

(1.1414 xoffset) -2 (.414x (clr) centre line radius this is the formula
example degree of elbow: 60=.577
45=.414
30=2.00
example in your situation
45 degree elbow 48x20=72, 48 + 24 half your check is 24=72 thats your centre line radius...
(1.414x36 offset)-2(.414x72)
=50.904-2(29.808)
=50.904-29.616
=21.288 thats the length of the duct in between your on your two 45 degree elbow...

i hope this help you...

This is confusing me? Firstly what is "-2" after multiplying the offset? Is the duct Dimension 48"x20"?? This is probably really simple but can you explain it to me please????! any help much appreciated!!!!

No books required, open a high school geometry book, look up similar triangles, Pythagoras theorem, and trig functions and how they interact with each other. It's all about solving for lengths of a right triangle.

I have a fair grasp of trigonometry now. Can anyone explain why this formula is what it is? I know that 1.414 is sin45 degrees twice. How Were The Other Numbers Figured out? Where is the right triangle being formed?