Question

The angles $A,B$ and $C$ of a triangle $ABC$ are in $A.P.$ If $b:c=\sqrt{3}:\sqrt{2}$, then the angle $A$ is

• A. ${30}^{\circ }$
• B. ${15}^{\circ }$
• C. ${75}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is C ${75}^{\circ }$

Let the angles be $a,a+d,a+2d$.

Then, $a+a+d+a+2d=180$

$=a+d=60$. So angle $B={60}^o$

Now, $\frac{b}{c}=\frac{\sin B}{\sin C}=\sqrt{\frac{3}{2}}$

$⟹\sin C=\sqrt{\frac{2}{3}}\times \frac{\sqrt{3}}{2}=\frac{1}{\sqrt{2}}$

$⟹C={45}^o$

So, $\angle A={75}^o$ $......AsA+B+C=180$

Hence, option C is correct.