c
\(\sqrt 2 \,\, = \,\,\frac{{\sin \,\,\left( {\frac{{60 + {\delta _m}}}{2}} \right)}}{{\sin \,\,\left( {\frac{{60}}{2}} \right)}}\)

\(\sqrt 2 \,\, \times \,\,\sin \,30\,\, = \,\,\,\sin \,\,\left( {\frac{{60 + {\delta _m}}}{2}} \right)\,\,\, \Rightarrow \,\,\,\,\sqrt 2 \,\, \times \,\,\,\frac{1}{2}\,\, = \,\,\sin \,\,\left( {\frac{{60 + {\delta _m}}}{2}} \right)\)

\(\sin \,\,{45^ \circ }\, = \,\,\sin \,\,\left( {\frac{{60 + {\delta _m}}}{2}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,{45^ \circ }\,\, = \,\,\,\frac{{60 + {\delta _m}}}{2}\,\,\, \Rightarrow \,\,\,{\delta _m} = \,\,{30^ \circ }\)

\({\delta _m} = \,\,2i\,\, - \,\,A\,\,\, \Rightarrow \,\,30\,\, = \,\,2\,\,i\,\, - \,\,60\,\,\, \Rightarrow \,\,\,i\,\, = \,\,{45^ \circ }\)