# Triangle problem

#### idontknow

Given triangle with lengths a,b,c , prove that the sum of two random chosen lengths is larger than the other length.

#### DarnItJimImAnEngineer

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 $\gamma \rightarrow 180Â°$.

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