Trig. Law of Cosines - Physics Forums: Physics, Astronomy, Math, & Philosophy Forums!

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#1
12-12-2006, 08:36 PM
 ashleebrook Junior Member Join Date: Dec 2006 Posts: 2
Trig. Law of Cosines

Show that any triangle with standard labeling...
a^2+b^2+c^2/2abc = cos(alpha)/a + cos(beta)/b + cos(gamma)/c

#2
12-13-2006, 05:00 PM
 HallsofIvy Senior Member Join Date: Oct 2006 Posts: 464

(a^2+b^2+c^2)/2abc = cos(alpha)/a + cos(beta)/b + cos(gamma)/c
which is rather different from what you wrote. (Notice the first parenthesis pair?)

Since you mention the cosine law in your title, I guess you know that

a^2= b^2+ c^2- 2bc cos(alpha)
b^2= a^2+ c^2- 2ac cos(beta)
c^2= a^2+ b^2- 2ab cos(gamma)

Add those 3 equations, simplify, and divide both sides by 2abc.

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