Need help with pre cal hw

1. A party of hikers walks 8 km from camp on 30 degrees, then turns and walks 6 km on course 160 degrees. Find the magnitude of the net displacement from camp.
2. A ship leaves port A and sails 61.1 km course 131 degrees 50' to point B. Then it sails 76.5 km on course 36 degrees 30' to point C. Find the bearing of point C from point A.

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asked by John
  1. note 160 = south - 20

    North distance = 8 cos 30 - 6 cos 20
    East distance = 8 sin 20 + 6 sin 20

    distance = sqrt (North^2 + east^2)

    2.
    call it 132 = south - 48
    north distance=-61.1cos 48 +76.5sin 36.5
    east distance =61.1sin48 +76.5cos 36.5
    tan theta = north/east

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    posted by Damon
  2. 1. I sketched a triangle, and noticed I could use the cosine law:

    R^2 = 8^2 + 6^2 - 2(8)(6)cos 50°
    = 38.2923...
    R = appr 6.189 km

    or

    use vectors
    first vector = (8cos30 , 8 sin 30) = (6.9282 , 4)
    2nd vector = (6cos160, 6sin 160) = (-5.63815.. , 2.05212)

    sum = ( 1.29004.... , 6.05212)

    magnitude = √( 1.29004..^2 + 5.05212^2)
    = appr 6.189

    Do the 2nd in the same way.

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    posted by Reiny
  3. LOL, physicist / mathematician again.

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    posted by Damon

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