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

In $\Delta ABC,$ if $a = 16, b = 24$ and $c = 20,$ then $\cos \frac{B}{2} = $

In a $\triangle ABC$,$\operatorname{cosec} A(\sin B \cos C + \cos B \sin C)$ is equal to

If the angles $A, B$ and $C$ of a triangle are in $A.P.$ and if $a, b$ and $c$ denote the length of the sides opposite to $A, B$ and $C$ respectively,then the value of $\frac{a}{b} \sin 2B + \frac{b}{a} \sin 2A$ is

If $ABCD$ is a cyclic quadrilateral with $AB=6, BC=4, CD=5, DA=3$ and $\angle ABC=\theta$,then $\cos \theta=$

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the sides of the triangle are