A student runs through a field 100m(E) then 200m(S) and finally 50(45 degrees S of E find his final position relative to his starting point?

Question

A student runs through a field 100m(E) then 200m(S) and finally 50(45 degrees S of E find his final position relative to his starting point?
please explain steps
Answer is 272(60 degrees S of E)

Henry · Answer

A = 100m[0o] B = 200m[270o] C = 50m[3i5o] D = A+B+C D=(100+200*cos270+50*cos315+i(sin270+50*sin315) D = (100+0+35.4) + i(-200-35.4) D = 135.4 - i235.4 = 272m[-60o] = 272m [60o S. of E.].