Answer
$$\,c = 6.46{\text{m, }}A = {53.1^ \circ },\,\,B = {81.3^ \circ }$$
Work Step by Step
$$\eqalign{
& C = {45.6^ \circ },\,\,\,b = 8.94{\text{m,}}\,\,\,a = 7.23{\text{m}} \cr
& {\text{Use the Law of cosines to find }}c \cr
& {c^2} = {a^2} + {b^2} - 2ab\cos C \cr
& {\text{Substitute}} \cr
& {c^2} = {\left( {7.23} \right)^2} + {\left( {8.94} \right)^2} - 2\left( {7.23} \right)\left( {8.94} \right)\cos \left( {{{45.6}^ \circ }} \right) \cr
& {\text{Use a calculator}} \cr
& {c^2} \approx 41.74934 \cr
& {\text{Take square roots and choose the positive root}} \cr
& c \approx 6.46{\text{m}} \cr
& \cr
& {\text{Calculate the angle }}A{\text{ using the law of sines}} \cr
& \frac{a}{{\sin A}} = \frac{c}{{\sin C}} \cr
& \sin A = \frac{{a\sin C}}{c} \cr
& \sin A = \frac{{7.23\sin \left( {{{45.6}^ \circ }} \right)}}{{6.46}} \cr
& \sin A \approx 0.799634 \cr
& A \approx {\sin ^{ - 1}}\left( {0.799634} \right) \cr
& A = {53.1^ \circ } \cr
& \cr
& {\text{Calculate }}B \cr
& B = {180^ \circ } - A - C \cr
& B = {180^ \circ } - {53.1^ \circ } - {45.6^ \circ } \cr
& B = {81.3^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& \,c = 6.46{\text{m, }}A = {53.1^ \circ },\,\,B = {81.3^ \circ } \cr} $$
