The direction of 12 m is towards west north with an angle of 20 with the y-axis or north.
The direction of 20 m is towards the south west with an angle of 40 with the x-axis or west.
From the given figure,
The angle between the 12 m and the west is,
[tex]\begin{gathered} \alpha=90^{\circ}-20^{\circ} \\ \alpha=70^{\circ} \end{gathered}[/tex]Thus, the angle between the 12 m and 20 m is,
[tex]\begin{gathered} \theta=\alpha+40^{\circ} \\ \theta=70^{\circ}+40^{\circ} \\ \theta=110^{\circ} \end{gathered}[/tex]The resultant of the 12 m walk and 20 m walk is,
[tex]R=\sqrt[]{A^2+B^2+2AB\cos (\theta)}[/tex]Substituting the known values,
[tex]\begin{gathered} R=\sqrt[]{12^2+20^2+2\times12\times20\times\cos (110^{\circ})} \\ R=19.5\text{ m} \end{gathered}[/tex]Thus, the magnitude of the resultant of R is 19.5 m.
