Answer
$$\,c = 348{\text{ft, }}A = {63^ \circ }45',\,\,B = {43^ \circ }35'$$
Work Step by Step
$$\eqalign{
& C = {72^ \circ }40'{\text{,}}\,\,\,a = 327{\text{ft,}}\,\,\,b = 251{\text{ft}} \cr
& {\text{Use the Law of cosines to find }}c \cr
& {c^2} = {a^2} + {b^2} - 2ab\cos C \cr
& {\text{Substitute}} \cr
& {c^2} = {\left( {327} \right)^2} + {\left( {251} \right)^2} - 2\left( {327} \right)\left( {251} \right)\cos \left( {{{72}^ \circ }40'} \right) \cr
& {\text{Use a calculator}} \cr
& {c^2} \approx 121023.5526 \cr
& {\text{Take square roots and choose the positive root}} \cr
& c \approx 348{\text{ft}} \cr
& \cr
& {\text{Calculate the angle }}A{\text{ using the law of sines}} \cr
& \frac{a}{{\sin A}} = \frac{c}{{\sin C}} \cr
& \sin A = \frac{{a\sin C}}{c} \cr
& \sin A = \frac{{327\sin \left( {{{72}^ \circ }40'} \right)}}{{348}} \cr
& {\text{Use a calculator}} \cr
& \sin A \approx 0.8969832062 \cr
& {\text{Use the inverse sine function}} \cr
& A \approx {\sin ^{ - 1}}\left( {0.8969832062} \right) \cr
& A = {63^ \circ }45' \cr
& \cr
& {\text{Calculate }}B \cr
& B = {180^ \circ } - A - C \cr
& B = {180^ \circ } - {63^ \circ }45' - {72^ \circ }40' \cr
& B = {43^ \circ }35' \cr
& \cr
& {\text{Answer}} \cr
& \,c = 348{\text{ft, }}A = {63^ \circ }45',\,\,B = {43^ \circ }35' \cr} $$
