My Math Forum Pythagorean theorem/Lesson Learned

 Geometry Geometry Math Forum

 February 16th, 2019, 01:46 PM #2 Global Moderator   Joined: May 2007 Posts: 6,822 Thanks: 723 The usual extension to the Pythagorean theorem is the law of cosines: $c^2=a^2+b^2-2ab\cos C$, where $C$ is the angle opposite side $c$. Last edited by skipjack; February 16th, 2019 at 05:20 PM.
 February 16th, 2019, 03:13 PM #3 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 Thanks for clarifying that. To be honest, I have difficulty understanding the law of cosines. I do use it, but sometimes I use it incorrectly. Mainly because it's hard for me to understand. Again, thanks for telling me that. I appreciate you and others here help me out with understanding mathematics.
February 16th, 2019, 05:48 PM   #4
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 Originally Posted by jnicholes I then found this formula that answered the question: Side * 2cos(angle)
That works, but the angle isn't the apex angle. If you want to use the apex angle, the
formula becomes side * 2sin(angle/2).

Quote:
 Originally Posted by jnicholes Eventually, I got it. This is what I came up with: (a+b) sin(angle/2)
That formula works only if a = b, so it can be written as (2a) sin(angle/2), which is equivalent to the formula I gave above.

Quote:
 Originally Posted by jnicholes Then, I tried something harder. . . . Here is what I came up with: a*cos(angle AC) + b*cos(angle BC) = c
That is usually written as c = a * cos(B) + b * cos(A). It's a standard result, but is often overlooked, perhaps because it doesn't seem to have a handy description or name.

 February 16th, 2019, 06:39 PM #5 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 @skipjack, you are correct with everything you just said. Thank you for telling me that. You just made me realize something. I went and did days of research and experimenting to try to find my own way, and when I do find my own way, and I share it, it turns out it was already figured out by someone else. To be honest, I do not know how I am coming up with this stuff without even knowing that it already existed. I guess I just like experimenting and learning how things work my own way. I learn from experience. It's just who I am. Thanks for the help and the input. I appreciate it. Jared
February 17th, 2019, 03:58 PM   #6
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 Originally Posted by jnicholes Thanks for clarifying that. To be honest, I have difficulty understanding the law of cosines. I do use it, but sometimes I use it incorrectly. Mainly because it's hard for me to understand. Again, thanks for telling me that. I appreciate you and others here help me out with understanding mathematics.
What about the cosine law is so hard to understand? I suggest you sketch a triangle and see how it works.

 February 17th, 2019, 05:06 PM #7 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 @mathman, I don't really understand it, because I didn't really learn about it well enough when I went through school. You have to understand I am mentally challenged, math is one of the area's I excel in, however, because of my disability, I was alternating between homeschool and regular school periodically. Because of this, I think I missed learning about certain math things, like the law of cosines. The Law of Sines, I just learned recently, to be honest. Would you mind explaining to me the law of cosines? It's difficult to understand because I never really learned it well enough. I know a little bit of it, but I don't know all of it. Jared
 February 17th, 2019, 05:59 PM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Google it; you'll get helpful sites like: https://betterexplained.com/articles/law-of-cosines/
 February 17th, 2019, 07:15 PM #9 Member   Joined: May 2018 From: Idaho, USA Posts: 65 Thanks: 7 Thanks, @Denis. I just looked it up. It's making more sense now. Thanks for helping out. Jared
 February 18th, 2019, 07:47 AM #10 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 cosine.jpg Code: c² = EB² + EA² = CB² - CE² + (CA - CE)² = a² - CE² + CA² - 2CE*CA + CE² = a² + b² - 2(a cos(C))*b = a² + b² - 2ab cos(C)

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