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    Obtuse versus acute cocked hat
    From: Bill Lionheart
    Date: 2019 Mar 21, 08:07 +0000

    How pointy is your hat?
    
    If the angles of a triangle were chosen from a uniform distribution
    obtuse triangles are more common. In a fix using three LOPs from
    observation of celestial bodies the azimuths are not chosen randomly,
    they are chosen from the bodies available for observation and the
    navigator's judgements as which to use. So in practice what is the
    ration observed in practice of obtuse to acute in practice?
    
    One reason I am asking is that for an acute triangle the weights in a
    weighted least squares problem can be adjusted so that the elliptical
    probability contour is circular. So if one can increase the accuracy
    of some LOPs, by taking n sights with a reduction in variance that
    goes as 1/(n-2), one can obtain more equal uncertainty in all
    directions. But for obtuse triangles the circumcentre lies outside the
    triangle and this makes the required weights negative. In practice I
    have seen a lot of obtuse cocked hats.
    
    Bill Lionheart
    

       
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