H$.$W$/$

In the figure below, a theodolite device was Installed at point C$,$ near the bank of a river at a distance of $\frac{?}{\text{b}\text{a}\text{r}}(6)$ meters from point A along the line $\frac{?}{\text{b}\text{a}\text{r}}(AB).$ Points $B$ and D were observed in the face$-$left position, with the horizontal reading for point B being $(00{00}^{\text{'}}{00}^{\text{'}\text{'}})$ and for point D being $(45{10}^{\text{'}}{30}^{\text{'}\text{'}}).$ After that, the same two points were observed In the face$-$right position, so the horizontal reading for point B was $(180{00}^{\text{'}}{20}^{\text{'}\text{'}})$ and for point D was $(225{10}^{\text{'}}{50}^{\text{'}\text{'}}).$ If the distance between points $B$ and $D$ is $12$ meters, find the width of the river.

$12$m