how to use the law of cosine?

Discussion in 'Archived Threads 2001-2004' started by felix_suwarno, Sep 12, 2002.

  1. felix_suwarno

    felix_suwarno Screenwriter

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    i have a triangle. side a=3. side b=4. side c=2.1 ( this one is on the opposite side of theta ).

    the formula is

    cos theta = ( (a*a) + (b*b) - (c*c) ) / (2ab)

    i got :

    cos theta = 0.8579166667

    now how to get the angle of theta?? i tried to do arc cos using my calculator, but the result is 0.5395954398

    i KNOW that the angle of theta should be 30.05 degree ( according to my protractor ).

    how to get 30.05 out of that calculation? is my calculator calculating the numbers in radian?

    btw this is for a comp graphics class
     
  2. NickSo

    NickSo Producer

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    Yeah, it looks like the resulting answer is in rads. I just checked what 30.05 in rads was, it was .52447144, pretty similar to what you got on the second answer...

    EDIT: Okay, i got it... I think, its not exact though. The answer was 30.92

    the formula i used was c^2=(a^2)+(b^2)-2(a)(c)cosC (i htink your formula is the same, just written differently.

    I came up with:
    2.1^2=(4^2)+(3^2)-2(4)(3)cosC
    2(4)(3)cosC = (16)+(9)-(4.41)
    24(cosC) = 20.59
    cosC = 20.59/24

    then i used cos^-1 on my calculator, and found 30.91653504
     
  3. Wayne Bundrick

    Wayne Bundrick Cinematographer

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    I got 30.92 degrees.
     
  4. felix_suwarno

    felix_suwarno Screenwriter

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    ahhh thanks for fast response. but how do i convert rad to degree?
     
  5. NickSo

    NickSo Producer

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    Well on my calculator, if you're in Degree mode, just type n the degree, and when you swithc to rads, itll display the degrees in Rads (mine's a SHARP).
    But to do it the long way, you take the degrees, multiply by Pi, and then divide by 180:
    [c]30.92(Pi)
    180[/c]
    Equals .539655804 rads
     
  6. Gary King

    Gary King Second Unit

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    Or you could do it the hard way and use a Taylor series to approximate acos (which is all the calculator is doing, anyway).

    I'd recommend you forget degrees exist and learn to use radians almost exclusively. Most graphics (and physics) equations that deal with angles will require radians.
     
  7. felix_suwarno

    felix_suwarno Screenwriter

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    ok for all of you, big thanks.
     
  8. John_Berger

    John_Berger Cinematographer

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    Boy, do I feel inadequate. I didn't understand a freakin' thing that was said. [​IMG]
    **sigh*
     
  9. NickSo

    NickSo Producer

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    John: its aight, i had to go find the law of cosines on the net to figure it out [​IMG]
     

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