The area of an isosceles triangle is $9 \, cm^2$. If the equal sides are $6 \, cm$ in length,the angle between them is .... $^\circ$.

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 $^{\circ}$)

Let $ABC$ be a triangle such that $AB=4, BC=5$ and $CA=6$. Choose points $D, E, F$ on $AB, BC, CA$ respectively,such that $AD=2, BE=2, CF=2$. Then find the ratio of the area of $\triangle DEF$ to the area of $\triangle ABC$.

In $\Delta ABC$,if the altitudes from $A, B, C$ to the opposite sides are in harmonic progression,then $\sin A, \sin B, \sin C$ are in ............. progression.

In $\triangle ABC$,$(r_1+r_2) \operatorname{cosec}^2 \frac{C}{2} =$

If the sides of a $\Delta$ are $(x^2 + x + 1)$,$(2x + 1)$,and $(x^2 - 1)$,then the greatest angle is.....$^o$