In a triangle $ABC$,with usual notations,if $a=5$,$b=7$,and $\sin A=\frac{3}{4}$,then the total number of triangles possible is:

The angles of a triangle are in the ratio $2:3:7$ and the radius of the circumscribed circle is $10 \text{ cm}$. The length of the smallest side is (in $\text{ cm}$)

In $\triangle ABC$,with usual notations,if $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$,then the value of $\cos A+\cos B+\cos C$ is

In a triangle $ABC$,if $r_1=2 r_2=3 r_3$,then $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=$

Let $ABC$ be a triangle such that $\angle ACB = \frac{\pi}{6}$ and let $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively. The value$(s)$ of $x$ for which $a = x^2+x+1, b = x^2-1$ and $c = 2x+1$ is (are)

If in $\triangle ABC$,with usual notations,the angles are in $A$.$P$.,then $\frac{a}{c} \sin 2C + \frac{c}{a} \sin 2A =$