While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 109 m at an angle θ = 30.0° north of east, and 156 m south. Find the resultant displacement from the cave entrance. The figure below suggests the situation but is not drawn to scale.

magnitude :
direction : ° south of east

2 answers

treating the vectors as complex numbers, we have

75i + 250 + 109cis(pi/6) - 156i
= 344.4 - 26.5i

or, in polar form,

345.4 @ E4.4°S
i don't understand the direction