Answer
$$a = 15.7{\text{m}},{\text{ }}B = {21.6^ \circ },\,\,C = {45.6^ \circ }$$
Work Step by Step
$$\eqalign{
& A = {\text{112}}.{\text{8}}^\circ ,\,\,b = {\text{6}}.{\text{28 m}},\,\,c = {\text{12}}.{\text{2 m}} \cr
& {\text{Use the Law of cosines to find }}a \cr
& {a^2} = {b^2} + {c^2} - 2bc\cos A \cr
& {\text{Substitute}} \cr
& {a^2} = {\left( {{\text{6}}.{\text{28}}} \right)^2} + {\left( {{\text{12}}.{\text{2}}} \right)^2} - 2\left( {{\text{6}}.{\text{28}}} \right)\left( {{\text{12}}.{\text{2}}} \right)\cos \left( {{\text{112}}.{\text{8}}^\circ } \right) \cr
& {\text{Use a calculator}} \cr
& {a^2} \approx 247.6581883 \cr
& {\text{Take square roots and choose the positive root}} \cr
& a \approx 15.7{\text{m}} \cr
& \cr
& {\text{Calculate the angle }}B{\text{ using the law of sines}} \cr
& \frac{b}{{\sin B}} = \frac{a}{{\sin A}} \cr
& \sin B = \frac{{b\sin A}}{a} \cr
& \sin B = \frac{{{\text{6}}.{\text{28}}\sin \left( {{\text{112}}.{\text{8}}^\circ } \right)}}{{15.7}} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 0.3687452606 \cr
& {\text{Use the inverse sine function}} \cr
& B = {21.6^ \circ } \cr
& \cr
& {\text{Calculate }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {\text{112}}.{\text{8}}^\circ - {21.6^ \circ } \cr
& C = {45.6^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& a = 15.7{\text{m}},{\text{ }}B = {21.6^ \circ },\,\,C = {45.6^ \circ } \cr} $$
