A grasshopper makes four jumps. The displacement vectors are (1) 27.0 cm, due west; (2) 23.0 cm, 35.0° south of west; (3) 28.0 cm, 55.0° south of east; and (4) 35.0 cm, 63.0° north of east. Find the magnitude and direction of the resultant displacement. Express the direction with respect to due west.

yes, this is a bit confusing problem with all its "... north of east ..." and "... south of west ...". If you place the grasshopper before his first jump onto the point x=0,y=0 of the rectangular coordinate system (like, X axis and Y axis), then his first jump is along the X axis in the positive direction. This is because it is assumed in this problem that you will select the following orientation of your coordinate system: positive X semi-axis is west, negative X semi-axis -- east, positive Y semi-axis -- north, negative Y semi-axis -- south. Please draw this coordinate system to see if it makes the solution more obvious.