Answer
$$b = 34.1{\text{cm}},{\text{ }}A = {5.19^ \circ },\,\,C = {6.61^ \circ }$$
Work Step by Step
$$\eqalign{
& B = {\text{168}}.{\text{2}}^\circ ,\,\,a = {\text{15}}.{\text{1 cm}},\,\,\,c = {\text{19}}.{\text{2 cm}} \cr
& {\text{Use the Law of cosines to find }}b \cr
& {b^2} = {a^2} + {c^2} - 2ac\cos B \cr
& {\text{Substitute}} \cr
& {b^2} = {\left( {{\text{15}}.{\text{1}}} \right)^2} + {\left( {{\text{19}}.{\text{2}}} \right)^2} - 2\left( {{\text{15}}.{\text{1}}} \right)\left( {{\text{19}}.{\text{2}}} \right)\cos \left( {{\text{168}}.{\text{2}}^\circ } \right) \cr
& {\text{Use a calculator}} \cr
& {b^2} \approx 1164.236467 \cr
& {\text{Take square roots and choose the positive root}} \cr
& b \approx 34.1{\text{cm}} \cr
& \cr
& {\text{Calculate the angle }}A{\text{ using the law of sines}} \cr
& \frac{{\sin A}}{a} = \frac{{\sin B}}{b} \cr
& \sin A = \frac{{a\sin B}}{b} \cr
& \sin A = \frac{{15.1\sin \left( {{\text{168}}.{\text{2}}^\circ } \right)}}{{34.1}} \cr
& {\text{Use a calculator}} \cr
& \sin A \approx 0.0905539707 \cr
& {\text{Use the inverse sine function}} \cr
& A \approx {5.19^ \circ } \cr
& \cr
& {\text{Calculate }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {5.19^ \circ } - {\text{168}}.{\text{2}}^\circ \cr
& C = {6.61^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& b = 34.1{\text{cm}},{\text{ }}A = {5.19^ \circ },\,\,C = {6.61^ \circ } \cr} $$
