Law of sines--ambiguous problem

Discussion in 'General Math' started by hgl, Jul 9, 2004.

  1. hgl

    hgl Guest

    a=65,c=62,h=63.5,C=78 degrees

    what is A?

    If there is no solution, why?
    hgl, Jul 9, 2004
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  2. hgl

    David Moran Guest

    By the Law of Sines,

    65/sin A=62/sin78, which is the same as 62sin A=65sin78 therefore sin
    A=1.0255. Since the range of sine is -1 to 1, there's no solution.

    David Moran, Jul 9, 2004
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  3. Do you mean ambiguous, or "overdetermined"? If the information given
    here were to be set down into equations... you will have more
    information than you need to define a triangle--and if any of your
    information turns out to be... well, inconsistent, then you don't have
    a solution that can satisfy all the equations (it's kind of like
    asking for a right triangle with an obtuse angle).

    Anyway, the way I understand it here, you have lengths of all three
    sides, which is sufficient to define a triangle. All you need to do is
    to calculate the triangle (which is quite trivial--a machine
    (specifically, my TI-83 calculator which has a triangle-solving
    program I made years ago) can do it), and see if the angle is
    consistent with the result you get.
    Andrew B. Park, Jul 9, 2004
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