In $\triangle ABC$,if $r_1: r_2 = 7: 8$ and $r_1: r_3 = 3: 4$,then $a: b: c =$

In a $\Delta ABC,$ if $a = 2x,$ $b = 2y$ and $\angle C = 120^\circ,$ then the area of the triangle is

The area of the triangle $ABC$ is $10\sqrt{3} \text{ cm}^2$,angle $B$ is $60^{\circ}$ and its perimeter is $20 \text{ cm}$. Then $\ell(AC) = $ (in $\text{ cm}$)

In $\triangle ABC$,with usual notations,$2ac \sin \left(\frac{1}{2}(A-B+C)\right)$ is equal to

In a triangle $ABC$,with usual notation,$\angle B = \pi/3$ and $\angle C = \pi/4$. If $D$ divides $BC$ internally in the ratio $1:3$,find the value of $\frac{\sin \angle BAD}{\sin \angle CAD}$.

In $\triangle ABC$ with the usual notations,if $\left(\tan \frac{A}{2}\right)\left(\tan \frac{B}{2}\right)=\frac{3}{4}$,then $a+b=\ldots$ (in $c$)