My Math Forum Detailed section of all triangles which have unexplained properties

 Trigonometry Trigonometry Math Forum

 January 11th, 2019, 05:56 PM #11 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 The inequalities $a+b>c,\, a+c>b,\, b+c>a$ are known as the triangle inequality. Your third and fourth identities can be written as $(c\times\sin B)^2+(c\times\cos B)^2=c^2$ and $(c\times\sin A)^2+(c\times\cos A)^2=c^2$ so that they hold for any value of $c$, not just when $c$ is 1. Hence my change to this effect in your previous list. As $c\times\sin B = b\times\sin C$, $(c\times\sin B)^2+(b\times\cos C)^2=b^2$ is equivalent to $(b\times\sin C)^2+(b\times\cos C)^2=b^2$, which can be simplified to $\sin^2\! C + \cos^2\! C = 1$. I think all the identities you listed can be found on Wikipedia. Thanks from topsquark
 January 13th, 2019, 09:52 AM #12 Newbie   Joined: Jan 2018 From: Ontario Posts: 11 Thanks: 0 Correction for the fourth line. $(b\times\cos A)^2+(a\times\cos B)^2=c^2$
 January 13th, 2019, 01:15 PM #13 Newbie   Joined: Jan 2018 From: Ontario Posts: 11 Thanks: 0 For side c so the base is not only 1the equations are: $(c\times\sin B)^2+(c\times\cos B)^2=c^2$ $(c\times\sin A)^2+(c\times\cos A)^2=c^2$
January 13th, 2019, 01:17 PM   #14
Newbie

Joined: Jan 2018
From: Ontario

Posts: 11
Thanks: 0

Quote:
 Originally Posted by skipjack The inequalities $a+b>c,\, a+c>b,\, b+c>a$ are known as the triangle inequality. Your third and fourth identities can be written as $(c\times\sin B)^2+(c\times\cos B)^2=c^2$ and $(c\times\sin A)^2+(c\times\cos A)^2=c^2$ so that they hold for any value of $c$, not just when $c$ is 1. Hence my change to this effect in your previous list. As $c\times\sin B = b\times\sin C$, $(c\times\sin B)^2+(b\times\cos C)^2=b^2$ is equivalent to $(b\times\sin C)^2+(b\times\cos C)^2=b^2$, which can be simplified to $\sin^2\! C + \cos^2\! C = 1$. I think all the identities you listed can be found on Wikipedia.
Thanks

 January 13th, 2019, 06:50 PM #15 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Regarde dans le dictionnaire Larousse
January 13th, 2019, 09:52 PM   #16
Global Moderator

Joined: Dec 2006

Posts: 20,972
Thanks: 2222

Quote:
 Originally Posted by Larrousse Correction for the fourth line. $(b\times\cos A)^2+(a\times\cos B)^2=c^2$
That's incorrect. I'm not sure what you intended.

January 14th, 2019, 12:52 AM   #17
Newbie

Joined: Jan 2018
From: Ontario

Posts: 11
Thanks: 0

Quote:
 Originally Posted by skipjack That's incorrect. I'm not sure what you intended.
It's an error, disregard it.

 Tags detailed, magical, properties, section, triangles, unexplained

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Carl James Mesaros Computer Science 2 April 13th, 2017 12:49 AM BenFRayfield Computer Science 0 February 11th, 2015 08:06 PM qskti Linear Algebra 0 January 9th, 2015 09:57 AM jonas Algebra 1 November 12th, 2009 10:55 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top