If in a triangle $A B C$, with usual notations, the angles are in A.P. and $\mathrm{b}: \mathrm{c}=\sqrt{3}:…

If in a triangle $A B C$, with usual notations, the angles are in A.P. and $\mathrm{b}: \mathrm{c}=\sqrt{3}: \sqrt{2}$, then angle. $\mathrm{A}=$
  1. $30^{\circ}$
  2. $60^{\circ}$
  3. $75^{\circ}$
  4. $45^{\circ}$

Solution

Since the angles are in A.P., therefore $B=60^{\circ}$ By sine rule, $\begin{aligned} & \frac{b}{c}=\frac{\sin B}{\sin C} \Rightarrow \frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{3}}{2 \sin C} \Rightarrow C=45^{\circ} \\ \therefore \quad & A=180^{\circ}-60^{\circ}-45^{\circ}=75^{\circ} \end{aligned}$

Asked in: MHT CET 2024 (11 May Shift 1)

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