Aspelunker is surveying a cave. she follows a passage 180 m straight west, then 230 m in a direction 45° east of south, and then 280 m at 30° east of north. after a fourth unmeasured displacement, she finds herself back where she started. a: use a scale drawing to determine the magnitude of the fourth displacement. express your answer using two significant figures.
b: determine the direction of the fourth displacement. express your answer using two significant figures.

A) D = 146.34m

B) α = 33.07° south of west

Explanation:

In the diagram you can see the position after each displacement.

Point A will be at (-180,0) in rectangular coordinates

Point B will be at (-180,0) + (230*cos(45), -230*sin(45))=(-17.365, -162.635)

Point C will be at Pb + (280*sin(30), 280*cos(30)) = (122.635, 79.852)

The fourth displacement will therefore be: (-122.635, -79.852).

The module of this vector is 146.34m

And the angle is 33.07° south of west

568.98

explanation:

its math