Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Determine the value of $B$

Applying Sine rule in $∆ABC$ having sides $a,b,c$

$$\begin{gathered} \Rightarrow \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\left[\text{Substitute the values}\right] \\ \Rightarrow \frac{2}{\left({\displaystyle \frac{2}{3}}\right)}=\frac{3}{\sin B};\left[\because \sin A=\frac{2}{3},a=2,b=3,\mathrm{given}\right] \\ \Rightarrow \sin B=1 \\ \Rightarrow \sin B=\sin \frac{\mathrm{\pi }}{2};\left[\because \sin \frac{\mathrm{\pi }}{2}=1\right] \\ \Rightarrow B=\frac{\mathrm{\pi }}{2} \\ \Rightarrow B=90° \end{gathered}$$

Hence, the correct option is (C)