We will have the following:
Magnitude:
[tex]x=\sqrt[]{(18.0+21.0\cdot\cos(40.0))^2+(-5.0+21.0\sin(40.0))^2}\Rightarrow x=35.13038857[/tex][tex]\Rightarrow x\approx35.1[/tex]
So, its magnitude is approximately 35.1 meters.
Now, we calculate its direction:
[tex]\tan (\theta)=\frac{21\sin(40)-5}{18+21\cos(40)}\Rightarrow\theta=\arctan (\frac{21\sin (40)-5}{18+21\cos (40)})[/tex][tex]\Rightarrow\theta=13.9995455\Rightarrow\theta\approx14.0[/tex]
So, the direction is approximately 14.0°.
***Screenshot***
