Aspelunker is surveying a cave. she follows a passage 180 m straight west, then 290 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. determine the direction of the fourth displacement? (degrees) (south of west)

The direction of the fourth displacement is θ = 12.775  ( south of west)

Explanation:

write down the values in the question,

The passage is 180m west, 290m in the direction 45° east of south, 280m at 30° east of north.

x = 290 × cos 45° + 280 × sin 30° -180

x=165.06 m

y= 280 cos ( 30° - 290 × sin (45°)

y= 37.426°

θ = tan ^-1 (y/x) = tan^-1 (37.426 / 165.06)

θ= 12.775° ( south of west)

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