Given:
[tex]\begin{gathered} \angle A=22^{\circ} \\ b=13 \\ c=20 \end{gathered}[/tex]
To find a:
Using the cosine formula,
[tex]\begin{gathered} a=\sqrt[]{b^2+c^2-2bc\cos A} \\ a=\sqrt[]{13^2+20^2-2(13)(20)\cos 22} \\ a=\sqrt[]{169+400-520\cos 22} \\ a=9.320 \\ a\approx9.3 \end{gathered}[/tex]
Hence, length of the unknown side is 9.3.
