While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 75.0 m north, 250 m east, 116 m at an angle 30.0° north of east, and 200 m south. Find the resultant displacement from the cave entrance.

Answer 1

X = hor. = 250 + 116cos30 = 350.46m.
Y = ver. = 116sin30 + 75 - 200 = -67m.

tanA = Y / X = -67 / 350.46 = -0.19118,
A = -10.82 deg.,CW = -10.82 + 360 = 349.2 deg.,CCW.

R = X / cosA = = 350.46 / cos349.2 = 357m. @ 349.2 deg.