Finding Magnitude and Direction problem?

Question

While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75 m north, 250 m east, 145 m at an angle 30° north of east, and 125 m south. Find the resultant displacement from the cave entrance.

1) Find Magnitude in m

2) Find Direction in°

Answer 1

If you plot/graph the distances to scale, then you will note that the displacement will be the hypotenuse of a right triangle with legs measuring 22.5 m and 375.5737 m.

Using the Pythagorean theorem, the displacement

D = sqrt(22.5^2 + 375.5737^2)

D = 376.25 m

and the direction is

tan X = 22.5/375.5737 = 0.0599

X = arc tan 0.0599

X = 3.43 degrees north of east