Without assigning any values to your parameters, perhaps this can provide some information
Simplify[
Reduce[{
ra == rc + db + da,
rb == rc + db,
da == Sqrt[ra^2 - (rc*Sin[i])^2] - Sqrt[rb^2 - (rc*Sin[i])^2],
db == Sqrt[rb^2 - (rc*Sin[i])^2] - rc*Cos[i]},
{da, db}],
Pi/180 <= i <= Pi/2]
That gives some warnings that it cannot find a single solution. But, with or without the Simplify, you might be able to look at the result of that, possibly provide some additional information about the domain of ra, rb, rc, da, db and provide it enough information that it could give you solutions for da and db.
You probably also want to change each of your Sums from
Ia = Sum[SA, {i, Pi/180, Pi/2}]
to
Ia = Sum[SA, {i, Pi/180, Pi/2, Pi/180}]
if you want it to sum every two degrees because otherwise it will only sum the values i=Pi/180 and i=Pi/180+1 and then stop.