Answer
$$54^\circ 21'$$
Work Step by Step
$$\eqalign{
& {\text{Let }}B = {\text{39}}^\circ {\text{5}}0',b = {\text{268 m}},a = {\text{34}}0{\text{ m}} \cr
& \cr
& {\text{Find }}A,{\text{ use the law of sines}} \cr
& \frac{{\sin A}}{a} = \frac{{\sin B}}{b} \cr
& \sin A = \frac{{a\sin B}}{b} \cr
& {\text{Substitute}} \cr
& \sin A = \frac{{\left( {{\text{34}}0{\text{m}}} \right)\sin \left( {{\text{39}}^\circ {\text{5}}0'} \right)}}{{{\text{268m}}}} \cr
& \cr
& {\text{Use a calculator}} \cr
& \sin A \approx 0.8126463826 \cr
& A \approx {\sin ^{ - 1}}\left( {0.8126463826} \right) \cr
& A \approx 54^\circ 21' \cr} $$
