\(\displaystyle{A}{B}=\sqrt{{{A}{C}^{{2}}+{B}{C}^{{2}}-{\left({2}\cdot{A}{C}\cdot{B}{C}{\cos}\angle{B}{C}{A}\right)}}}\)

\(\displaystyle{A}{B}=\sqrt{{{47}^{{2}}+{33}^{{2}}-{\left({2}\cdot{47}\cdot{33}{\cos{{70}}}^{\circ}\right)}}}\)

\(\displaystyle{A}{B}=\sqrt{{{2237.05}}}\)

\(\displaystyle{A}{B}={47.29}\)

Using the cosine law,

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left(\frac{{{B}{C}^{{2}}+{A}{B}^{{2}}-{A}{C}^{{2}}}}{{{2}\cdot{B}{C}\cdot{A}{B}}}\right)}}\)

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left(\frac{{{33}^{{2}}+{47.29}^{{2}}-{47}^{{2}}}}{{{2}\cdot{33}\cdot{47.29}}}\right)}}\)

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left({0.3576}\right)}}\)

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}=}{69.04}^{\circ}\)

\(\displaystyle{A}{B}=\sqrt{{{47}^{{2}}+{33}^{{2}}-{\left({2}\cdot{47}\cdot{33}{\cos{{70}}}^{\circ}\right)}}}\)

\(\displaystyle{A}{B}=\sqrt{{{2237.05}}}\)

\(\displaystyle{A}{B}={47.29}\)

Using the cosine law,

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left(\frac{{{B}{C}^{{2}}+{A}{B}^{{2}}-{A}{C}^{{2}}}}{{{2}\cdot{B}{C}\cdot{A}{B}}}\right)}}\)

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left(\frac{{{33}^{{2}}+{47.29}^{{2}}-{47}^{{2}}}}{{{2}\cdot{33}\cdot{47.29}}}\right)}}\)

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}{\left({0.3576}\right)}}\)

\(\displaystyle\angle{A}{B}{C}={{\cos}^{{-{{1}}}}=}{69.04}^{\circ}\)