Question

In a triangle $ABC$ if $a=2,b=3$ and $\sin A=2/3$, then what is angle $B$ equal to?

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{6}$

Answer 1

The correct option is B $\frac{\pi }{2}$

In $△ABCa=2,b=3$ and $\sin A=2/3$

By applying sine law

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

$\to \frac{2}{2/3}=\frac{3}{\sin B}\to \sin B=1\Rightarrow B=\frac{\pi }{2}$.