In triangle $ABC$,if $C=120^{\circ}$,$c=\sqrt{19}$,and $b=3$,then $a=$

In a triangle $ABC$,with usual notation,$\angle B = \pi/3$ and $\angle C = \pi/4$. If $D$ divides $BC$ internally in the ratio $1:3$,find the value of $\frac{\sin \angle BAD}{\sin \angle CAD}$.

If in a $\Delta ABC$,$a, b, c$ are in $A.P.$,then $\tan \frac{A}{2} \tan \frac{C}{2} = $

In $\triangle ABC$,if $r_1 = 2r_2 = 3r_3$,then $b : c$ equals

$A$ triangle can be uniquely determined by its

In $\triangle ABC$,if $a=13, b=14$ and $\cos \frac{C}{2}=\frac{3}{\sqrt{13}}$,then $2r_1=$