In a triangle $ABC$,$a = 5, b = 7$ and $\sin A = \frac{3}{4}$,how many such triangles are possible?

In $\triangle ABC$, find the value of $\frac{1+\cos C}{r_1+r_2}+\frac{1+\cos A}{r_2+r_3}+\frac{1+\cos B}{r_1+r_3}$.

If $\cot \left(\frac{A}{2}\right)=\sqrt{\frac{1+a}{1-a}} \cdot \cot \left(\frac{\theta}{2}\right)$,then $\cos \theta=$

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

In a $\triangle ABC$,the mid-point of $BC$ is $D$. If $AD$ is perpendicular to $AC$,then $\cos A \cos C=$

Let $f, g, h$ be the lengths of the perpendiculars from the circumcentre of the $\Delta ABC$ on the sides $a, b$ and $c$ respectively. If $\frac{a}{f} + \frac{b}{g} + \frac{c}{h} = \lambda \frac{abc}{fgh}$,then the value of $\lambda$ is: