In a triangle $ABC$,$\frac{a}{b}=2+\sqrt{3}$ and $\angle C=60^{\circ}$. Then the measure of $\angle A$ is (in $^{\circ}$)

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 $\text{ units}$)

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

If two angles of $\triangle ABC$ are $\frac{\pi}{4}$ and $\frac{\pi}{3}$,then the ratio of the smallest and greatest side is

In $\triangle ABC$,if $a=2(\sqrt{3}+1)$,$B=45^{\circ}$ and $C=60^{\circ}$,then the area (in sq.units) of that triangle is

With usual notations,if the lengths of the sides of a triangle are $7 \text{ cm}$,$4\sqrt{3} \text{ cm}$,and $\sqrt{13} \text{ cm}$,then the measure of the smallest angle is