Triangle problem

Dec 2015
1,085
169
Earth
Given triangle with lengths a,b,c , prove that the sum of two random chosen lengths is larger than the other length.
 
Jun 2019
493
262
USA
Law of cosines: $c^2 = a^2+b^2 -2ab \cos \gamma ~\leq ~a^2+b^2$
Square of the sum: $(a+b)^2 = a^2+b^2+2ab ~\geq ~a^2+b^2$

Also, drawing a triangle as $\gamma \rightarrow 180°$.
 
  • Like
Reactions: 1 person