Answer
$$C = {57.36^ \circ },\,\,\,b = 11.13{\text{ft, }}\,c = 11.55{\text{ft}}$$
Work Step by Step
$$\eqalign{
& A = {68.41^ \circ },\,\,\,B = {54.23^ \circ },\,\,\,a = 12.75{\text{ft}} \cr
& \cr
& {\text{Use the law of sines to find side }}b \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& b = \frac{{a\sin B}}{{\sin A}} \cr
& b = \frac{{12.75\sin \left( {{{54.23}^ \circ }} \right)}}{{\sin \left( {{{68.41}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& b \approx 11.13{\text{ft}} \cr
& \cr
& {\text{Find }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {68.41^ \circ } - {54.23^ \circ } \cr
& C = {57.36^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{a}{{\sin A}} = \frac{c}{{\sin C}} \cr
& c = \frac{{a\sin C}}{{\sin A}} \cr
& c = \frac{{12.75\sin \left( {{{57.36}^ \circ }} \right)}}{{\sin {{68.41}^ \circ }}} \cr
& c = 11.55{\text{ft}} \cr
& \cr
& {\text{Answer}} \cr
& C = {57.36^ \circ },\,\,\,b = 11.13{\text{ft, }}\,c = 11.55{\text{ft}} \cr} $$
