We need to find the angle x, so let's find the angle of the first two vectors:
[tex]\theta_1=\frac{270+360}{2}=315[/tex][tex]\theta_2=60[/tex]
so:
[tex]v_x=10cos(315)+15cos(60)=14.57[/tex][tex]v_y=10sin(315)+15sin(60)=5.91[/tex]
Therefore, the angle is:
[tex]\begin{gathered} \theta_r=tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{5.91}{14.57}) \\ \theta_r=22.11^{\circ} \end{gathered}[/tex]
Answer:
The direction of the car's resultant vector is 22.11⁰
