Answer
$$26.52^\circ $$
Work Step by Step
$$\eqalign{
& a = {\text{14}}.{\text{8 m}},b = {\text{19}}.{\text{7 m}},c = {\text{31}}.{\text{8 m}} \cr
& \cr
& {\text{Find }}B,{\text{ use the law of cosines}} \cr
& {b^2} = {a^2} + {c^2} - 2ac\cos B \cr
& \cos B = \frac{{{a^2} + {c^2} - {b^2}}}{{2ac}} \cr
& \cr
& {\text{Substitute}} \cr
& \cos B = \frac{{{{\left( {{\text{14}}.{\text{8}}} \right)}^2} + {{\left( {{\text{31}}.{\text{8}}} \right)}^2} - {{\left( {{\text{19}}.{\text{7}}} \right)}^2}}}{{2\left( {{\text{14}}.{\text{8}}} \right)\left( {{\text{31}}.{\text{8}}} \right)}} \cr
& {\text{Use a calculator}} \cr
& \cos B \approx 0.8947284549 \cr
& {\text{Use the inverse cosine function}} \cr
& B \approx {\cos ^{ - 1}}\left( {0.8947284549} \right) \cr
& B \approx 26.52^\circ \cr} $$
