An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 38 steps at an angle 45 degrees north of east, then 81 steps at an angle 60 degrees north of west, then 51 steps due south. Assume his steps all have equal length. Save him from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut.
A) What is the magnitude of the displacement that will return the explorer to his hut?
B) What is the direction of the displacement that will return the explorer to his hut?