Well here's my guess, 1/3 of 24 is 8 so this is an 8/12 pitch. An 8/12 is about 33-3/4 degrees.
This is one way of figuring the length, just remember Pythagoras. A squared plus B squared equals C squared. The diagram shows how I found the lengths of each of the three sides. I then divided the length of the rafter side by the length of the run side. This gives me the ratio of the rafter to the run, the line length ratio.
For every foot (or inch, or whatever increment) of horizontal run, the rafter is 1.2017 units long for an 8/12 pitch. You are 12' of horizontal run so 144"x1.2017= measuring along the top, roughly 173-1/16".