In $\Delta ABC$,if $2s = a + b + c$,then the value of $\frac{s(s - a)}{bc} - \frac{(s - b)(s - c)}{bc} = $

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 $b=2, c=3$ and $\angle B=\frac{\pi}{6}$,then $a$ satisfies the equation

If in a triangle $ABC$,$\frac{\sin A}{4} = \frac{\sin B}{5} = \frac{\sin C}{6}$,then the value of $\cos A + \cos B + \cos C$ is equal to

The sides of a triangle are $\sin \alpha$,$\cos \alpha$,and $\sqrt{1 + \sin \alpha \cos \alpha}$ for some $0 < \alpha < \frac{\pi}{2}$. Then the greatest angle of the triangle is.....$^o$

If the angles of a triangle are in the ratio $1 : 2 : 7,$ then the ratio of its greatest side to the least side is