Answer
$$B = {27.19^ \circ },\,\,\,\,C = {10.68^ \circ }$$
Work Step by Step
$$\eqalign{
& A = {142.13^ \circ },\,\,\,\,\,b = 5.432{\text{ft,}}\,\,\,\,a = 7.297{\text{ft}} \cr
& \cr
& {\text{Use the law of sines to find the angle of }}B \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& \sin B = \frac{{b\sin A}}{a} \cr
& \sin B = \frac{{5.432\sin \left( {{{142.13}^ \circ }} \right)}}{{7.297}} \cr
& {\text{Use a calculator}} \cr
& \sin B = 0.45697 \cr
& {\text{Use the inverse sine function}} \cr
& B = {\sin ^{ - 1}}\left( {0.45697} \right) \cr
& B = {27.19^ \circ } \cr
& \cr
& {\text{Calculating }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {142.13^ \circ } - {27.19^ \circ } \cr
& C = {10.68^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& B = {27.19^ \circ },\,\,\,\,C = {10.68^ \circ } \cr} $$
