The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1+\sin \theta \cos \theta}$ for some $0<\theta<\frac{\pi}{2}$, then the greatest angle of a triangle is

For the triangle ABC , with usual notations, if the angles $A, B, C$ are in A.P. and $\mathrm{m} \angle \mathrm{A}=30^{\circ}, \mathrm{c}=3$, then the values of a and b are respectively

If $(a+b) \cos C+(b+c) \cos A+(c+a) \cos B=72$ and if $a=18, b=24$, then area of the triangle $A B C$ is

If the angles of a triangle are in the ratio $4: 1: 1$, then the ratio of the longest side to the perimeter is