The sides of a $\triangle ABC$ are given by $a=3, b=5$ and $c=3$. Then,$\cos A=$

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

The lengths of the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the lengths of the sides of the triangle (in units) are

In a triangle $ABC$,$s\left[\frac{r_1-r}{a}+\frac{r_2-r}{b}+\frac{r_3-r}{c}\right]=$

In a triangle,if $b=5, c=6$,and $\tan \frac{A}{2}=\frac{1}{\sqrt{2}}$,then $a=$

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 $\frac{\cos A}{p_1} + \frac{\cos B}{p_2} + \frac{\cos C}{p_3}$.