In a triangle $ABC$ with usual notations,if $a=13, b=14, c=15$,then $\sin A=$

In triangle $ABC$, $a=2$, $b=3$ and $\sin A=\frac{2}{3}$, then $B$ is equal to (in $^{\circ}$)

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

In a triangle $PQR$,let $\angle PQR = 30^{\circ}$ and the sides $PQ$ and $QR$ have lengths $10\sqrt{3}$ and $10$,respectively. Then,which of the following statement$(s)$ is (are) $TRUE$?
$(A)$ $\angle QPR = 45^{\circ}$
$(B)$ The area of the triangle $PQR$ is $25\sqrt{3}$ and $\angle QRP = 120^{\circ}$
$(C)$ The radius of the incircle of the triangle $PQR$ is $10\sqrt{3} - 15$
$(D)$ The area of the circumcircle of the triangle $PQR$ is $100\pi$

In $\triangle ABC$,with usual notations,if $b=3$,$c=8$,and $m\angle A=60^{\circ}$,then the circumradius of the triangle is . . . . . . units.

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is