5. Suppose $a, b$, and $c$ are the sides of a triangle opposite angles $\alpha, \beta$, and $\gamma$ respectively. If $\cos \beta<0$ and $\cos \alpha<\cos \gamma$, arrange $a, b$, and $c$ in increasing order.
Answer: $c, a, b$
Solution: $\beta$ must be obtuse and therefore the largest angle, and so $b$ is the longest side. As for $a$ and $c$, since $\alpha$ and $\gamma$ must both be acute, cos is decreasing and thus $\alpha>\gamma$, so $a>c$.