Answer
$$55.55{\text{m}}$$
Work Step by Step
$$\eqalign{
& A = {\text{51}}^\circ {\text{2}}0\prime ,c = {\text{68}}.{\text{3 m}},b = {\text{58}}.{\text{2 m}} \cr
& \cr
& {\text{Find }}a,{\text{ use the law of cosines}} \cr
& {a^2} = {b^2} + {c^2} - 2bc\cos A \cr
& {a^2} = {\left( {{\text{58}}.{\text{2}}} \right)^2} + {\left( {{\text{68}}.{\text{3}}} \right)^2} - 2\left( {{\text{58}}.{\text{2}}} \right)\left( {{\text{68}}.{\text{3}}} \right)\cos \left( {{\text{51}}^\circ {\text{2}}0\prime } \right) \cr
& \cr
& {\text{Use a calculator}} \cr
& {a^2} = 3084.986335 \cr
& {\text{Take square roots and choose the positive root}} \cr
& a \approx 55.55{\text{m}} \cr} $$
