In a $\triangle ABC$,if $a=13, b=14$ and $c=15$,then $\sin(\frac{A}{2})$ is:

Let $ABC$ be an acute-angled triangle with area $R$. Then,$\sqrt{a^2 b^2-4 R^2}+\sqrt{b^2 c^2-4 R^2}+\sqrt{c^2 a^2-4 R^2} = $

Let $a, b$ and $c$ be the lengths of the sides of a triangle $ABC$ such that $\frac{a+b}{7} = \frac{b+c}{8} = \frac{c+a}{9}$. If $r$ and $R$ are the inradius and circumradius of the triangle $ABC$,respectively,then the value of $\frac{R}{r}$ is equal to

In $\Delta ABC$, if $a^{2} \cos^{2} A - b^{2} - c^{2} = 0$, then

In $\triangle ABC$, with usual notations, $(a + b + c)(b + c - a)(c + a - b)(a + b - c) = 3b^2c^2$, then $\angle A = $

In a $\Delta ABC$,$a, c, A$ are given and $b_1, b_2$ are two values of the third side $b$ such that $b_2 = 2b_1$. Then $\sin A = $