This

theta = (At100*rc*Pc*MwB)/(3*dbm*Pb*MwC);

appears to be causing you problems. If I remove that, then evaluate the rest of your assignments, and finally

NMinimize[{Norm[R2]+Norm[R1], 0<theta<1 && 0.4<dam<2 && dbm>0}, {theta, dam, dbm}]

quickly returns

{1.34609*10^-8, {theta -> 0.60021, dam -> 0.886882, dbm -> 0.761926}}

If instead I do not remove the assignment to theta then

NMinimize[{Norm[R2]+Norm[R1], 0<theta<1 && 0.4<dam<2 && dbm>0}, {dam, dbm}]

returns

{0.0526246, {dam -> 0.791757, dbm -> 0.341362}}

and

(At100*rc*Pc*MwB)/(3*dbm*Pb*MwC) /. dbm -> 0.3413622051761988`

shows

0.999987

so that does not find nearly as good a minimum and theta is up against your boundary

Problem solved.. thank Bill for your time! Finally it was easy!

Also you forgot that in the particular domain rc=47 (known) takes place

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.

Everything seems fine until you get to

db = Sqrt[rb^2 - (rc*Sin[i])^2] - rc*Cos[i]

To do that it looks up the value of rb which is rc + db. To do that it looks up the value of rc which is 47. Then it looks up the value of db. You have started defining the value of db and so it starts all over again with your db=Sqrt[...]. And it does all this over and over and over until after doing this 1024 times it puts up a warning and usually fails.

Perhaps this is only a small typo. Or perhaps you didn't mean to define db in terms of db.

Can you formulate your problem where the value of variables aren't defined in terms of the value of those same variables?