If $A+B=\frac{\pi}{4}$, then $(1+\tan A)(1+\tan B)$ is equal to

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