The given case is SSS (three sides) so use the Law of Cosines: \(\displaystyle{b}^{{2}}={a}^{{2}}+{c}^{{2}}-{2}{a}{\mathcal{{o}}}{s}{B}\)

Solve for B.

\(\displaystyle{2}{a}{\mathcal{{o}}}{s}{B}={a}^{{2}}+{c}^{{2}}-{b}^{{2}}\)

\(\displaystyle{\cos{{B}}}=\frac{{{a}^{{2}}+{c}^{{2}}-{b}^{{2}}}}{{2}}{a}{c}\)

\(\displaystyle{m}{<}{B}={\left({\cos}^{{-{{1}}}}\right)}{\left(\frac{{{a}^{{2}}+{c}^{{2}}-{b}^{{2}}}}{{2ac}}\right)}\)

\(\displaystyle{m}{<}{B}={\left({\cos}^{{-{{1}}}}\right)}{\left(\frac{{{15}^{{2}}+{10}^{{2}}-{14}^{{2}}}}{{2}{\left({15}\right)}{\left({10}\right)}}\right)}\)

\(\displaystyle{m}{<}{B}={{\cos}^{{-{{1}}}}{\left(\frac{{129}}{{300}}\right)}}\)

Use a calculator in DEGREE mode: \(\displaystyle{m}∠{B}≈{64.5}°\)