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25 April, 20:39

A spelunker 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)

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  1. 25 April, 20:41
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    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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