Question

In triangle $ABC,a=2,b=3$ and $\sin A=\frac{2}{3}$, then $B$ is equal to

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C ${90}^{\circ }$

Using sine rules
$\frac{\sin A}{a}=\frac{\sin B}{b}$
$\Rightarrow \frac{2/3}{2}=\frac{\sin B}{3}$
$\Rightarrow \sin B=1$
$\Rightarrow B={90}^{\circ }$