With usual notations in $\Delta \mathrm{ABC}, \mathrm{a}=3, \mathrm{c}=2$ and $\sin \mathrm{C}=\frac{2}{3}$,…

With usual notations in $\Delta \mathrm{ABC}, \mathrm{a}=3, \mathrm{c}=2$ and $\sin \mathrm{C}=\frac{2}{3}$, then $\angle \mathrm{A}=$
  1. $\frac{\pi^{c}}{4}$
  2. $\frac{\pi^{c}}{3}$
  3. $\frac{\pi^{c}}{2}$
  4. $\frac{\pi^{c}}{6}$

Solution

By sine Rule, we write $\therefore \frac{\sin A}{3}=\frac{\left(\frac{2}{3}\right)}{2} \Rightarrow \frac{\sin A}{3}=\frac{1}{3} \Rightarrow \sin A=1 \Rightarrow A=90^{\circ}=\frac{\pi}{2}$

Asked in: MHT CET 2020 (12 Oct Shift 2)

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