If the lengths of the sides of a triangle are $3, 5, 7$,then the largest angle of the triangle is

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

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 $\frac{\sin \angle BAD}{\sin \angle CAD}$.

In a $\triangle ABC$,if $a=4, b=5$ and $c=7$,then $\sin \left(\frac{A}{2}\right) = $

In a right-angled $\triangle ABC$, the measures of the angles are in an Arithmetic Progression ($A$.$P$.). If its smallest side is $4 \text{ units}$, then the area of $\triangle ABC$ is:

If the angles of a triangle are in the ratio $4:1:1$,then the ratio of the longest side to its perimeter is