If in a triangle $ABC$,$a=2$,$b=3$ and $c=4$,then $\tan \left(\frac{A}{2}\right) = $

Let $ABC$ be a triangle such that $AB = BC$. Let $F$ be the mid-point of $AB$ and $X$ be a point on $BC$ such that $FX$ is perpendicular to $AB$. If $BX = 3XC$,then the ratio $BC / AC$ equals

If $4$ times the area of a $\triangle ABC$ is $c^2-(a-b)^2$,then $\sin C$ is equal to:

If in the $\Delta ABC$,$AB = 2BC$,then find the ratio $\tan \frac{B}{2} : \cot \left( \frac{C - A}{2} \right)$.

For the triangle $ABC$,with usual notations,if the angles $A, B, C$ are in $A.P.$ and $m \angle A = 30^{\circ}, c = 3$,then the values of $a$ and $b$ are respectively

The angles of a triangle are in the ratio $3: 5: 10$. Then the ratio of the smallest side to the greatest side is: