8. Let $0<\alpha \leqslant \beta \leqslant \gamma$, and $\alpha+\beta+\gamma=\pi$, then the range of $\min \left\{\frac{\sin \beta}{\sin \alpha}, \frac{\sin \gamma}{\sin \beta}\right\}$ is
8. $\left[1, \frac{1+\sqrt{5}}{2}\right)$ Analysis: Let $\alpha, \beta, \gamma$ be the three interior angles of a triangle, with their opposite sides being $a, b, c$, respectively. Then $\frac{\sin \beta}{\sin \alpha}=\frac{b}{a}, \frac{\sin \gamma}{\sin \beta}=\frac{c}{b}$. Let $\lambda=\min \left\{\frac{b}{a}, \frac{c}{b}\right\}$. By $0c \geqslant \lambda^{2} a \Rightarrow \lambda+1>\lambda^{2} \Rightarrow \frac{1-\sqrt{5}}{2}<\lambda<\frac{1+\sqrt{5}}{2}$, hence $\lambda \in\left[1, \frac{1+\sqrt{5}}{2}\right)$.