Answer
$$B = 17.3^\circ ,\,\,\,C = 137.5^\circ ,\,\,\,\,c = 11{\text{yd}}$$
Work Step by Step
$$\eqalign{
& A = {\text{25}}.{\text{2}}^\circ ,a = {\text{6}}.{\text{92 yd}},b = {\text{4}}.{\text{82 yd}} \cr
& {\text{Calculate the angle }}B{\text{ using the law of sines}} \cr
& \frac{{\sin B}}{b} = \frac{{\sin A}}{a} \cr
& \sin B = \frac{{b\sin A}}{a} \cr
& \sin B = \frac{{{\text{4}}.{\text{82}}\sin \left( {{\text{25}}.{\text{2}}^\circ } \right)}}{{6.92}} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 0.2965688129 \cr
& {\text{Use the inverse sine function}} \cr
& B \approx 17.3^\circ \cr
& \cr
& {\text{Calculate the angle }}C \cr
& C = 180^\circ - A - B \cr
& C = 180^\circ - {\text{25}}.{\text{2}}^\circ - 17.3^\circ \cr
& C = 137.5^\circ \cr
& \cr
& {\text{Calculate the side }}c{\text{ using the law of sines}} \cr
& \frac{c}{{\sin C}} = \frac{a}{{\sin A}} \cr
& c = \frac{{a\sin C}}{{\sin A}} \cr
& c = \frac{{{\text{6}}.{\text{92}}\sin \left( {137.5^\circ } \right)}}{{\sin \left( {{\text{25}}.{\text{2}}^\circ } \right)}} \cr
& c \approx 11{\text{yd}} \cr
& \cr
& {\text{Answer}} \cr
& B = 17.3^\circ ,\,\,\,C = 137.5^\circ ,\,\,\,\,c = 11{\text{yd}} \cr} $$
