## Precalculus (6th Edition) Blitzer

Using the ratio $\frac{a}{\sin A}$ or $\frac{10}{\sin 150{}^\circ }$ We will use the law of sines to find B. \begin{align} & \frac{a}{\sin A}=\frac{b}{\sin B} \\ & \frac{10}{\sin 150{}^\circ }=\frac{30}{\sin B} \\ & \sin B=\frac{30\sin 150{}^\circ }{10} \\ & \sin B=1.5 \end{align} As we know that the sine can never exceed 1, therefore, there is no angle B for which $\sin B=1.5$.