Answer
$$A = {34.72^ \circ },\,\,\,a = 3326.3{\text{ft}},\,\,\,\,c = 5703.88{\text{ft}}$$
Work Step by Step
$$\eqalign{
& B = {42.88^ \circ },\,\,\,C = {102.40^ \circ }{\text{,}}\,\,\,b = 3974{\text{ft}} \cr
& \cr
& {\text{Find }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {42.88^ \circ } - {102.40^ \circ } \cr
& A = {34.72^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}a \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& a = \frac{{b\sin A}}{{\sin B}} \cr
& a = \frac{{3974\sin \left( {{{34.72}^ \circ }} \right)}}{{\sin \left( {{{42.88}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& a = 3326.3{\text{ft}} \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr
& c = \frac{{b\sin C}}{{\sin B}} \cr
& c = \frac{{3974\sin \left( {{{102.40}^ \circ }} \right)}}{{\sin \left( {{{42.88}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& c = 5703.88{\text{ft}} \cr
& \cr
& {\text{Answer}} \cr
& A = {34.72^ \circ },\,\,\,a = 3326.3{\text{ft}},\,\,\,\,c = 5703.88{\text{ft}} \cr} $$
