The total displacement east is: <span> <span>15 cos(45) + 15
= 25.607 m
The total displacement north is:
15 sin(45)
= 10.607 m
The magnitude of the total displacement is:
sqrt(25.607^2 + 10.607^2) <span>= 27.717 m = 27.7 m</span>
Its direction is N x E where:
tan(x) = 25.607 / 10.607 <span>x = 67.5 deg
The return displacement is therefore of the same magnitude
but in the opposite direction. <span>Displacement 27.7 m, direction S 67.5 deg W</span></span></span></span>