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Math Help - Very Hard Practice Problem

  1. #1
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    Very Hard Practice Problem

    Centrepoint tower in Sydney has a viewing platform located 268 metres above sea level. A tourist on the observation deck notices two boats on Sydney harbour. From the tourist's position:

    The bearing of Boat A is 130^{\circ} at an angle of depression of 35^{\circ}.
    The bearing of Boat A is 200^{\circ} at an angle of depression of 42^{\circ}.

    Calculate the distance between the boats to the nearest metre.


    The math most likely involves simply Ratio / Sine Law / Cosine Law calculations, so the math part shouldn't be a problem. The problem is drawing a proper diagram to model the question. All I've got so far is the attached. Can anyone help me with simply visualizing what the question asks? What does it even mean for the boat to be a bear of X degrees?
    Attached Thumbnails Attached Thumbnails Very Hard Practice Problem-trig.jpg  
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  2. #2
    Junior Member slider142's Avatar
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    The bearing is the planar angle from the observer. That is, placing the base of the observation tower in the center of a clockface, a person would say "a ship at 2 o'clock" for a ship in the direction of the number 2 on the clock face. Replace the clock numbers with angle degrees.
    Thus, your diagram is missing the essential fact that the boats are not lying on the same side of that triangle; they are separated in a second direction.
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  3. #3
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    I got an answer of approximately 397m. That look about right?
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