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A ship is sighted directly east of a lighthouse. Another ship, which is 20m away from the first ship, is observed at a bearing of N25degreesE from the lighthouse. If the first ship is 4.1 km away from the lighthouse, what is the distance of the second ship from the lighthouse?

  • trigonometry -

    angle at ship B
    (sin 25)/20 = (sin A)/4.1
    sin A = .0866
    A = 4.97 deg
    angle at ship A
    A = 180 - 25 - 4.97 = 150.03 degrees
    then law of cosines
    d^2 = 20^2 + 4.1^2 - 2(20)(4.1)cosA

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