Answer
$${\text{58}}{\text{.6ft}}$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle we have:}} \cr
& B = 58.4^\circ ,\,\,\,C = 27.9^\circ ,\,\,\,a = 125{\text{ft,}}\,\,\,c = ? \cr
& \cr
& {\text{Calculate }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - 58.4^\circ - 27.9^\circ \cr
& A = 93.7^\circ \cr
& \cr
& {\text{Calculate the side }}c{\text{ using the law of sines}} \cr
& \frac{c}{{\sin C}} = \frac{a}{{\sin A}} \cr
& c = \frac{{a\sin C}}{{\sin A}} \cr
& c = \frac{{125\sin \left( {27.9^\circ } \right)}}{{\sin \left( {93.7^\circ } \right)}} \cr
& c \approx 58.6{\text{ft}} \cr
& \cr
& {\text{The distance from }}A{\text{ to }}B{\text{ is 58}}{\text{.6ft}} \cr} $$
