Answer
$$B = 37.77^\circ ,\,\,\,C = 45.43^\circ ,\,\,\,c = 4.174{\text{ft}}$$
Work Step by Step
$$\eqalign{
& A = {\text{96}}.{\text{8}}0^\circ ,\,\,\,\,\,b = {\text{3}}.{\text{589 ft}},\,\,\,\,a = {\text{5}}.{\text{818 ft}} \cr
& {\text{Use the law of sines to find the angle of }}B \cr
& \frac{{\sin B}}{b} = \frac{{\sin A}}{a} \cr
& \sin B = \frac{{b\sin A}}{a} \cr
& {\text{Substituting }} \cr
& \sin B = \frac{{\left( {{\text{3}}.{\text{589}}} \right)\sin \left( {{\text{96}}.{\text{8}}0^\circ } \right)}}{{{\text{5}}.{\text{818}}}} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 0.6125392246 \cr
& B \approx {\sin ^{ - 1}}\left( {0.6125392246} \right) \cr
& B \approx 37.77^\circ \cr
& \cr
& {\text{Calculate the angle of }}C \cr
& C = 180^\circ - A - B \cr
& C = 180^\circ - {\text{96}}.{\text{8}}0^\circ - 37.77^\circ \cr
& C = 45.43^\circ \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{c}{{\sin C}} = \frac{a}{{\sin A}} \cr
& c = \frac{{a\sin C}}{{\sin A}} \cr
& c = \frac{{{\text{5}}.{\text{818}}\sin \left( {45.43^\circ } \right)}}{{\sin \left( {{\text{96}}.{\text{8}}0^\circ } \right)}} \cr
& c \approx 4.174{\text{ft}} \cr
& \cr
& {\text{Answer}} \cr
& B = 37.77^\circ ,\,\,\,C = 45.43^\circ ,\,\,\,c = 4.174{\text{ft}} \cr} $$
