In a triangle $ABC$,if $\frac{\sin A - \sin C}{\cos C - \cos A} = \cot B$,then $A, B, C$ are in

In triangle $ABC$ with usual notations $b=\sqrt{3}$,$c=1$,and $m \angle A=30^{\circ}$,then the largest angle of the triangle is (in $^{\circ}$)

If the angles of a triangle are in the ratio $1:2:3$,then their corresponding sides are in the ratio

In a $\triangle ABC$,if $a+3b=3c$,then $\sin \frac{A}{2} =$

In $\Delta ABC$,$\frac{\sin B}{\sin (A + B)} = $

If the area of a triangle $ABC$ is $4\sqrt{5} \text{ sq. units}$, the length of the side $CA$ is $6 \text{ units}$, and $\tan \frac{B}{2} = \frac{\sqrt{5}}{4}$, then the length of its smallest side is: (in $\text{ units}$)