In $\Delta ABC$ with usual notations $a=4, b=3, \angle A=60^{\circ}$,then $c$ is a root of the equation

If the lengths of the sides of a triangle are $7 \, cm$,$4\sqrt{3} \, cm$,and $\sqrt{13} \, cm$,then the smallest angle is .....$^o$.

If $p_1, p_2, p_3$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively and if $\Delta$ is the area of the triangle,$S$ is the semi-perimeter of the triangle,then find the value of $\frac{\cos A}{p_1} + \frac{\cos B}{p_2} + \frac{\cos C}{p_3}$.

In a triangle $ABC$,if $2r_1 = 3r_2 = r_3$,then $a : b : c =$

If in a $\Delta ABC$,$\frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c}$,then the triangle is

If $A, B, C$ are angles of a triangle,then $\sin 2A + \sin 2B - \sin 2C$ is equal to