A uniform rectangular board OCDH with weight $W=30N$ is hinged along OH at equilibrium. Rope $1(AC)$ is under tension of $T_1=300N$ and Rope $2(DB)$ is under tension of $T_2.$ Hint: write down coordinates of C and D $.$

$($a$)$ Draw free body diagrams of the board, the two ropes and supports at A and B$.(10\%)$

$($b$)$ Find the angle $$ between the board and Rope $1$

$($c$)$ Find the angle $$ between Ropes $1$ and $2.(10\%)$

$($d$)$ Find the vector moment of $T_1$ about point H$.(5\%)$

$($e$)$ Find the vector moment of $T_1$ about point C$.(5\%)$

$($f$)$ Find the vector moment of $T_1$ about the hinge. $(5\%)$

$($g$)$ Find the vector tension $T_2.(5\%)$

$($h$)$ Find the vectors force and moment supported by the hinge. $(10\%)$