cosfi = 0.2;
tanfi = Tan[ArcCos[cosfi]];
resr = Solve[tanfi == (X/r), 
            r][[1]];
eta = 
        Simplify[((Sqrt[(r^2) + (X^2)])/((Sqrt[(r^2) + (X^2)]) + r)) /. resr, 
          X > 0];
Print["η= ", eta]