$1.($b$)$ The water gate $\backslash ($ A B C $\backslash )$ shown in Figure $1$ below is pivoted at $\backslash ($ B $\backslash )$ and opens by itself when the level $\backslash ($ H $\backslash )$ exceeds $2$ m $.$ What is the length $\backslash ($ B C $\backslash )?$

$($b$)$

Figure: $1($a$)$ Automatic gate and $($b$)$ pressure distribution on it$.$