With usual notations,if the angles $A, B, C$ of a $\triangle ABC$ are in $A$.$P$. and $b:c = \sqrt{3}:\sqrt{2}$,then $\angle A=$ (in $^{\circ}$)

In a $\triangle ABC$,the sides $a, b, c$ are in $A$.$P$. if and only if $r_1, r_2, r_3$ are in

In a triangle $ABC$, with the usual notations, $\angle B = \frac{\pi}{3}$ and $\angle C = \frac{\pi}{4}$. If $D$ divides $BC$ internally in the ratio $1:3$, then $\frac{\sin \angle BAD}{\sin \angle CAD} =$

If two sides of a triangle are $\sqrt{3}-2$ and $\sqrt{3}+2$ units and their included angle is $60^{\circ}$,then the third side of the triangle is

Let $ABC$ and $ABC^{\prime}$ be two non-congruent triangles with sides $AB=4$,$AC=AC^{\prime}=2\sqrt{2}$ and $\angle B=30^{\circ}$. The absolute value of the difference between the areas of these triangles is

In a $\triangle ABC$,if $a^4+b^4+c^4=2b^2c^2+2a^2b^2$,then $B=$