Point A has an unknown elevation. The instrument was set $1\mathrm{.}17m$ above point $B$ and point A was observed at an inclination angle of $42.$ After that, the instrument was moved towards point A and was set $1\mathrm{.}31m$ above point $C$ and point A was observed at an inclination angle of $68.$ If the distance between points $B$ and $C$ is $20m,$ what is the elevation of point A assuming that points $B$ and $C$ are of the same elevation and at elevation $0m.$