From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometre stone on the opposite sides of the aeroplane are found to be $\mathrm{\alpha }$ and $\mathrm{\beta }$. Find the height of the aeroplane (in km) if $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$, both are at $45°$.

The angle of elevation and depression of the top and bottom of a lighthouse from the top of a building $60 \mathrm{m}$ are $30°$ and $60°$ respectively. Find:

i) The difference between the heights of the lighthouse and the building.

ii) Distance between the lighthouse and the building,