If in a triangle $ABC$,$b = \sqrt{3}$,$c = 1$ and $B - C = 90^{\circ}$,then $\angle A$ is .....$^{\circ}$.

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 $\triangle ABC$,if $(a+c)^2 = b^2 + 3ca$,then $\frac{a+c}{2R} =$

In a triangle $ABC$,if $\sin A \sin B = \frac{ab}{c^2}$,then the triangle is

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

In a triangle $ABC$ with usual notations,if $a:b:c = 7:8:9$,then $\cos A : \cos B : \cos C =$