anglepvcroofroofingshed
I am building an A-frame PVC greenhouse. I plan to make the pitch 45 degrees for each side. I have a 10 foot gap across from each side of the wall.
How do I calculator the exact length of each half of the roof? I know there's Pythagoras Theorem (a2 +b2 = c2) but I am unsure how to apply it because I only know "A" and the 45 degree Angle, but not "B" or "C".
Thanks for any help!!
You're probably looking for an elastomeric roof coating.
Primarily, you'll need to clean the roof, repair and fill any cracks/gaps/etc and remove any of the peeling drylok, apply an appropriate primer meeting the manufacturer's suggestions, then apply at least two coats of the roof coating. It would also be recommended that any sloping/drainage issues be addressed as well in order to avoid heavy pooling, where possible.
As usual, cheaper is rarely better when it comes to roof coatings. A white coating tends to last longer and reduce roof temperatures (which should also help with interior temperatures).
I call them manufacture burn holes, I see them in most roofs even roofs only 1 year old, it is normally where there are either loose stone or poor seal of the stones on the shingle and with out the stones there is no protection and the sun will burn right thru the asphalt, it looks like your in this picture had some help with insects or yellow jackets, normally it just goes to the fiber or the shingle below, here is picture of one year old roof, just starting to deteriorate, 
Best Answer
If it's a 45 degree angle, B=A.
Or you can set any value you please for roof height. You don't need to know any trig, nobody cares what the angle is. People who do roofs work in rise/run ratio, not angles.
The Pythagorean Theorem requires one corner be a regular square corner (90 degrees. Fit it to your roof one of two ways:
Since in comments you say you are stuck with 45 degree angles*, here's how you use diagram A to do that. You've already established your bottom edge is 10' so c=10'. That is a stocking size, and let's say your PVC pipe does not have a flare on the end that you'd have to cut off (otherwise you'd need to recalc). a and b are the same since your roof is symmetrical, so you plug into Pythagoras's Theorom (with a few substitutions):
That 7/8 inches will getcha. Remember these measurements are from actual corners, so when choosing PVC length you need to measure the connectors to see how far the pipe stops short of the actual corner. PVC elbows are not made for building structures, so the manufacturers don't think about these things.
If you want to get good at that, talk to the people doing geodesic domes. They have to get the numbers right for the structure to be stable.