The vector will be represent (not accurately) like the diagram below:
Now, from the expression
[tex]\theta=\tan ^{-1}(\frac{v_x}{v_y})[/tex]
we get the pink angle, but we need the green angle. To get the correct one we calculate the pink one and then we find its supplementary angle; let's do that:
[tex]\begin{gathered} \theta=\tan ^{-1}(\frac{11.1}{43}) \\ \theta=14.47 \end{gathered}[/tex]
Now, the green angle will be:
[tex]180-14.47=165.53[/tex]
Therefore the direction of the vector is 165.53°
