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

If the angles of a triangle $ABC$ are in the ratio $1: 2: 3$,then the corresponding sides are in the ratio

Points $D$ and $E$ are taken on the side $BC$ of a triangle $ABC$ such that $BD = DE = EC$. If $\angle BAD = x$,$\angle DAE = y$,and $\angle EAC = z$,then the value of $\frac{\sin(x + y)\sin(y + z)}{\sin x \sin z}$ is:

In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $\angle C$ is equal to: (in $^{\circ}$)

With usual notations in $\triangle ABC$,if $\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}$,then $a^2, b^2, c^2$ are in

In triangle $ABC$,if $A + C = 2B$,then $\frac{a + c}{\sqrt{a^2 - ac + c^2}}$ is equal to