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