In $\triangle ABC$,we are given that $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$. Then,the measure of $\angle C$ is $....^{\circ}$

The upper $\frac{3}{4}$th portion of a vertical pole subtends an angle $\tan^{-1}\left(\frac{3}{5}\right)$ at a point in the horizontal plane through its foot and at a distance $40 \ m$ from the foot. $A$ possible height of the vertical pole is $....... \ m$.

In a triangle $ABC$,if $A, B, C$ are in arithmetic progression and $\cos A + \cos B + \cos C = \frac{1 + \sqrt{2} + \sqrt{3}}{2 \sqrt{2}}$,then $\tan A =$

In a $\triangle ABC$,the expression $\frac{a}{\tan A} + \frac{b}{\tan B} + \frac{c}{\tan C}$ is equal to:

In $\triangle ABC$,if $B=90^{\circ}$,then $2(r+R)=$

If $A, B, C$ are the angles of a triangle,then $\frac{\sin A+\sin B+\sin C}{\sin ^2 \frac{A}{2}-\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}-1} =$