To solve this problem we will make a diagram in the Cartesian plane that will allow us to find and understand more accurately the displacement and the angle of rotation.
According to Pythagoras, the distance traveled would be equivalent to
[tex]d = \sqrt{(2.7)^2+(3.5)^2}[/tex]
[tex]d = 4.4 miles[/tex]
The individual had a displacement of 4.4 thousand from the starting point.
Now the angle [tex]\theta[/tex] plus the previously given angle will allow us to find the direction of travel.
[tex]tan\theta = \frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
[tex]tan\theta = \frac{3.5}{2.7}[/tex]
[tex]\theta = tan^{-1} (\frac{3.5}{2.7})[/tex]
[tex]\theta = 52.35\°[/tex]
[tex]\angle =[/tex] [tex]\theta + 35 = 52.35+35 = 87.35\°[/tex]
Therefore the net direction of the man is S 87.35° W
