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Math Help - Proving

  1. #1
    Junior Member ihmth's Avatar
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    Jan 2008
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    Proving

    "Right Spherical Triangle"

    Prove: C = 90degrees, A = 120degrees, a = 100degrees
    Answer is no solution

    sin a = sin A * sin c
    sin a = tan b * ctn B
    sin b = sin B * sin c
    sin b = tan a * ctn A
    cos c = cos a * cos b
    cos c = ctn A * ctn B
    cos A = cos a * sin B
    cos A = tan b * ctn c
    cos B = cos b * sin A
    cos B = tan a * ctn c

    What I have done is this: so using sin a = sin A * sin c
    sin100 = sin120 * sinc.....sinc = 1.137158043 so we know that it has no solution, because the range of sine is [-1,1] and sinc > 1.btw, is this correct? and if so, is this the right way to pove it?
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  2. #2
    Junior Member ihmth's Avatar
    Joined
    Jan 2008
    Posts
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    Ok I'm wrong. Already look at the answer on the book.
    so A = 180 - 120 = 60
    > I subtracted 120/100 from 180, because I need to choose the shortest arc length.
    a = 180 - 100 = 80

    I should use sinb = tana*cotA

    log sinb = log tana*cotA
    log sinb = log tana + log cotA

    log tana = .75368
    log cotA = 9.76144 - 10

    log sinb = 0.51512
    sinb = 3.27431155
    so b = impossible

    therefore: no solution

    My question is: Why do I have to use log?
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