Results 1 to 3 of 3

Math Help - LAw of sines and Law of Cosines

  1. #1
    Junior Member
    Joined
    Sep 2007
    From
    Oregon, West Coast ^_^
    Posts
    50

    Exclamation LAw of sines and Law of Cosines

    Could someone solve for x using 2 different methods- Law of Sines and Law of cOSINES. And also, can someone explain to me the difference between the two, and how you know which one to use- law of sines or law of cosines or both. If someone could solve this step by step, I'd appreciate it. I really don't know how to do this.




    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by peachgal View Post
    Could someone solve for x using 2 different methods- Law of Sines and Law of cOSINES. And also, can someone explain to me the difference between the two, and how you know which one to use- law of sines or law of cosines or both. If someone could solve this step by step, I'd appreciate it. I really don't know how to do this.




    Thanks
    Given the amount of available data:

    The cosine rule can be used in three different ways. The following leads to the simplest calculation:

    From cosine rule: x^2 = 25^2 + 28^2 - 2(25)(28) \cos 37^0 \therefore x^2 = ........ \therefore x = ........


    These two each lead to more difficult calculations:

    From cosine rule: 28^2 = x^2 + 25^2 - 2(x)(25) \cos 81^0. Now re-arrange to get a quadratic equation and solve for x using the quadratic formula.


    From cosine rule: 25^2 = x^2 + 28^2 - 2(x)(28) \cos 62^0. Now re-arrange to get a quadratic equation and solve for x using the quadratic formula.


    The sine rule can be used in two different ways. Both lead to equally simple calculations:


    From sine rule: \frac{x}{\sin 37^0} = \frac{25}{\sin 62^0} \therefore x = .......


    From sine rule: \frac{x}{\sin 37^0} = \frac{28}{\sin 81^0} \therefore x = .........


    All five applications will lead to the same value of x.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2007
    Posts
    144
    In general with reference to Attachment;

    If two sides and the included angle are given (e.g. a,c and B ares given) use the cosine rule.

    If no angles are known use the cosine rule (re-arrange to make cos\theta the subject where \theta~ is the angle to be determined).

    If a side and the opposite angle are given (e.g. a and A are given) use the sine rule.
    Attached Thumbnails Attached Thumbnails LAw of sines and Law of Cosines-untitled.bmp  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. law of sines and law of cosines
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 28th 2009, 05:26 AM
  2. precalc help (law of sines and cosines)
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 22nd 2009, 02:17 PM
  3. Law of Sines and Cosines
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 23rd 2008, 04:49 AM
  4. Law of Sines/Cosines
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 8th 2007, 05:03 PM
  5. Law of Sines/Cosines
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 2nd 2007, 08:51 PM

Search Tags


/mathhelpforum @mathhelpforum