Step 1

Using the cosine law,

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

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

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

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

Step 2

Using the cosine law,

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

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

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

Using the cosine law,

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

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

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

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

Step 2

Using the cosine law,

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

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

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