Given:
[tex]A=30^{\circ},b=40ft,a=10ft[/tex]
The triangle is constructed as
Use the law of sine,
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \frac{\sin30^{\circ}}{10}=\frac{\sin B}{40}=\frac{\sin C}{c} \\ \text{Take,}\frac{\sin30^{\circ}}{10}=\frac{\sin B}{40} \\ \sin B=\frac{40}{10}\cdot\frac{1}{2} \\ \sin B=2 \end{gathered}[/tex]
As, we know that,
[tex]\begin{gathered} -1\leq\sin x\leq1 \\ It\text{ gives, }\sin B=2\text{ has no solution} \end{gathered}[/tex]
So, the given triangle can not be constructed.
Hence, the given triangle has no solution.
