Question

If $b=3,c=4$ and $B=\pi /3$ then find the number of triangles that can be constructed

Answer 1

Given, $b=3,c=4,B=\frac{pi}{3}$

We have,
$\frac{\sin B}{b}=\frac{\sin C}{c}$
$\Rightarrow \frac{\sin \left(\pi /3\right)}{3}=\frac{\sin C}{4}$
$\Rightarrow \sin C=\frac{2}{\sqrt{3}}>1$ ,which is not possible.

Hence, no triangle is possible.