Answer
$$C = {91.9^ \circ },\,\,\,\,AB = 847{\text{ft}},\,\,\,\,BC = 489.7{\text{ft}}$$
Work Step by Step
$$\eqalign{
& A = {35.3^ \circ },\,\,\,B = {52.8^ \circ }{\text{,}}\,\,\,AC = 675{\text{ft}} \cr
& {\text{The side }}AC{\text{ is }}b = 675{\text{ft}} \cr
& \cr
& {\text{Find }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {35.3^ \circ } - {52.8^ \circ } \cr
& C = {91.9^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}a{\text{ or }}BC \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& a = \frac{{b\sin A}}{{\sin B}} \cr
& a = \frac{{675\sin \left( {{{35.3}^ \circ }} \right)}}{{\sin \left( {{{52.8}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& a = 489.7{\text{ft}} \cr
& BC = 489.7{\text{ft}} \cr
& \cr
& {\text{Use the law of sines to find side }}c{\text{ or }}AB \cr
& \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr
& c = \frac{{b\sin C}}{{\sin B}} \cr
& c = \frac{{675\sin \left( {{{91.9}^ \circ }} \right)}}{{\sin \left( {{{52.8}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& c = 847{\text{ft}} \cr
& AB = 847{\text{ft}} \cr
& \cr
& {\text{Answer}} \cr
& C = {91.9^ \circ },\,\,\,\,AB = 847{\text{ft}},\,\,\,\,BC = 489.7{\text{ft}} \cr} $$