Tuesday, June 20, 2006

The Law of Cosines

This week I'd like to prove the Law of Cosines.

The Law of Cosines states that given any triangle with side lengths a, b and c and opposing angles A, B and C



First we'll divide the triangle into two right triangles by drawing the line that passes through B and is perpendicular to b.



Now we have a right triangle with c as the hypotenuse. And so according to the Pythagorean Theorem



The last step uses the result shown in the previous post which was that

at

6 comments:

  1. Anonymous9/23/10, 1:02 PM

    Brilliant! Thanks so much :)

    ReplyDelete
  2. Anonymous11/22/10, 10:35 PM

    Hello,

    I have a message for the webmaster/admin here at mathproofs.blogspot.com.

    May I use some of the information from this post right above if I give a backlink back to your website?

    Thanks,
    Jules

    ReplyDelete
  3. Anonymous3/11/12, 6:48 PM

    This was really helpful. Thank you!

    ReplyDelete
  4. Servant_of_Liberty3/28/12, 1:25 PM

    Thanks for the help! This proof helped me to understand the lesson I'm reading in College Trigonometry.

    ReplyDelete
  5. Anonymous5/17/12, 5:09 PM

    Dont you need to now prove it in case Angle C is obtuse or right?

    ReplyDelete
  6. Unknown5/5/13, 2:48 PM

    What are the steps that go with it, like, we split the triangle in 2 by the 8.1 theorem, that was just totally an example and 8.1 doesn't even cover that, but what are the reasons to all of those steps??

    ReplyDelete