Answer
$$b = 9.53{\text{in}},{\text{ }}A = {64.6^ \circ },\,\,C = {40.6^ \circ }$$
Work Step by Step
$$\eqalign{
& B = {\text{74}}.{\text{8}}^\circ ,a = {\text{8}}.{\text{92 in}}.,c = {\text{6}}.{\text{43in}} \cr
& \cr
& {\text{Use the Law of cosines to find }}b \cr
& {b^2} = {a^2} + {c^2} - 2ac\cos B \cr
& {\text{Substitute}} \cr
& {b^2} = {\left( {{\text{8}}.{\text{92}}} \right)^2} + {\left( {{\text{6}}.{\text{43}}} \right)^2} - 2\left( {{\text{8}}.{\text{92}}} \right)\left( {{\text{6}}.{\text{43}}} \right)\cos \left( {{\text{74}}.{\text{8}}^\circ } \right) \cr
& {\text{Use a calculator}} \cr
& {b^2} \approx 90.83526469 \cr
& {\text{Take square roots and choose the positive root}} \cr
& b \approx 9.53{\text{in}} \cr
& \cr
& {\text{Calculate the angle }}A{\text{ using the law of sines}} \cr
& \frac{{\sin A}}{a} = \frac{{\sin B}}{b} \cr
& \sin A = \frac{{a\sin B}}{b} \cr
& \sin A = \frac{{{\text{8}}.{\text{92}}\sin \left( {{\text{74}}.{\text{8}}^\circ } \right)}}{{9.53}} \cr
& {\text{Use a calculator}} \cr
& \sin A \approx 0.903247338 \cr
& {\text{Use the inverse sine function}} \cr
& A \approx {64.6^ \circ } \cr
& \cr
& {\text{Calculate }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {64.6^ \circ } - {\text{74}}.{\text{8}}^\circ \cr
& C = {40.6^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& b = 9.53{\text{in}},{\text{ }}A = {64.6^ \circ },\,\,C = {40.6^ \circ } \cr} $$
