If [tex]\cos \theta\ \textless \ 0 [/tex], then angle [tex]\theta[/tex] is obtuse and triangle with sides a, b, c is obtuse triangle. In an arbitrary triangle can be only one obtuse angle, and the side which lies opposite to the largest angle is the largest. Then since angle [tex]\theta[/tex] is opposite the side of length a you can conclude that a>c and a>b.
