Answer
$$A = {56^ \circ }00',\,\,\,\,AB = 361{\text{ft}},\,\,\,\,BC = 308{\text{ft}}$$
Work Step by Step
$$\eqalign{
& B = {20^ \circ }50',\,\,\,C = {103^ \circ }10'{\text{,}}\,\,\,AC = 132{\text{ft}} \cr
& {\text{The side }}AC{\text{ is }}b = 132{\text{ft}} \cr
& \cr
& {\text{Find }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {20^ \circ }50' - {103^ \circ }10' \cr
& A = {56^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}a{\text{ or }}BC \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& a = \frac{{b\sin A}}{{\sin B}} \cr
& a = \frac{{132\sin \left( {{{56}^ \circ }} \right)}}{{\sin \left( {{{20}^ \circ }50'} \right)}} \cr
& {\text{Use a calculator}} \cr
& a = 307.698{\text{ft}} \cr
& BC = 308{\text{ft}} \cr
& \cr
& {\text{Use the law of sines to find side }}c{\text{ or }}AB \cr
& \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr
& c = \frac{{b\sin C}}{{\sin B}} \cr
& c = \frac{{132\sin \left( {{{103}^ \circ }10'} \right)}}{{\sin \left( {{{20}^ \circ }50'} \right)}} \cr
& {\text{Use a calculator}} \cr
& c = 361.3{\text{ft}} \cr
& AB = 361{\text{ft}} \cr
& \cr
& {\text{Answer}} \cr
& A = {56^ \circ }00',\,\,\,\,AB = 361{\text{ft}},\,\,\,\,BC = 308{\text{ft}} \cr} $$
