## Precalculus (6th Edition) Blitzer

For any triangle, The law of sines states that: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\operatorname{sinC}}$ Using the law of sines we get, \begin{align} & \frac{a}{\sin A}=\frac{c}{\sin C} \\ & \frac{3}{\sin A}=\frac{1}{\sin 50{}^\circ } \\ & 3\cdot \sin 50{}^\circ =\sin A \\ & \sin A\approx 2.30 \end{align} Since, $\sin A\approx 2.30$ is not possible as the value of sine cannot exceed 1. So, the triangle with this measure is not possible to construct. Hence, no such triangle exists.