Precalculus

A plane flies 30 mi on a bearing of 200 degrees and then turns and flies 40 mi on a bearing of 10 degrees. Find the resultant displacement vector as a distance and bearing.

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  1. resultant
    = 30(cos200, sin200) + 40(cos10, sin10)
    = (-28.19-10.26) + (39.39 , 6.946
    = (11.20 , -3.315)

    magnitude = √(11.20^2 + (-3.315)^2) = 11.68 miles
    bearing:
    tanØ = -3.315/11.2 = ...
    Ø = 343.5°

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