# Chapter 6 - Review Exercises - Page 798: 7

No such triangle exists.

#### Work Step by Step

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.

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