If he travels 7km N40 degree west and 10km east, find the resultant displacement.

Draw the diagram. Using the law of cosines, the displacement z can be found via

z^2 = 7^2 + 10^2 - 2*7*10 cos50°

or, using components, the final location (x,y) is
(x,y) = (-7sin40°,7cos40°)+(10,0)
at an angle θ from the positive x-axis such that
tanθ = y/x