In a $\triangle ABC$,if $a=5, b=6, c=7$,then the length of the median drawn from $B$ is

If $\cot \left(\frac{A}{2}\right)=\sqrt{\frac{1+a}{1-a}} \cdot \cot \left(\frac{\theta}{2}\right)$,then $\cos \theta=$

In $\triangle ABC$,if $4r_1 = 5r_2 = 6r_3$,then $\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} =$

If in a $\Delta ABC$,$\angle A = 45^\circ$,$\angle C = 60^\circ$,then $a + c\sqrt{2} = $

In a triangle $ABC,$ if $a \sin A = b \sin B,$ then the nature of the triangle is:

In a $\Delta ABC$,if two sides $b$ and $c$ and an angle $B$ are given.
Statement $-1$: Let $b = 5 \ cm, c = 3 \ cm$ and $\angle B = 60^\circ$. The total number of possible triangles is $2$.
Statement $-2$: If $c \sin B < b < c$ and $B$ is an acute angle,then there are two possible values of $\angle C$.