In a $\Delta ABC,$ if $(\sin A + \sin B + \sin C)(\sin A + \sin B - \sin C) = 3\sin A\sin B,$ then the angle $C$ is equal to

In a $\triangle ABC$,the altitudes from $B$ and $C$ to the opposite sides are not shorter than their respective opposite sides. Then,one of the angles of $\triangle ABC$ is $........^{\circ}$

In $\triangle ABC$,$\angle B=60^{\circ}$ and $\angle A=75^{\circ}$. If a point $D$ divides $BC$ in the ratio $2:3$,then $\sin \angle BAD : \sin \angle CAD=$

In $\triangle ABC$, with usual notations, if $a = 4$, $b = 5$, and $c = 6$, then $\cos A$ and $\cos C$ are calculated using the Law of Cosines. Find the value of $\cos C$ and $\cos A$ to determine the relationship between $\angle C$ and $\angle A$.

In a $\Delta ABC,$ if $b = 20, c = 21$ and $\sin A = 3/5$,then $a = $

In $\triangle ABC$,with usual notations,if $\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c}$,then $m \angle C$ is equal to