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

A tower $$T_1$$ of the height $$60 \mathrm{~m}$$ is located exactly opposite to a tower $$T_2$$ of height $$80 \mathrm{~m}$$ on a straight road. From the top of $$T_1$$, if the angle of depression of the foot of $$T_2$$ is twice the angle of elevation of the top of $$T_2$$, then the width (in $$\mathrm{m}$$) of the road between the feet of the towers $$T_1$$ and $$T_2$$ is

If $$A, B, C \in[0, \pi]$$ and if $$A, B, C$$ are in $$\mathrm{AP}$$, then $$\frac{\sin A+\sin C}{\cos A+\cos C}$$ is equal to

If $$\alpha,\beta,\gamma \in[0,\pi]$$ and if $$\alpha,\beta,\gamma$$ are in AP, then $${{\sin \alpha - \sin \gamma } \over {\cos \gamma - \cos \alpha }}$$ is equal to