A force $P$ is applied to a bent rodABC, which is supported in the way as shown.

$($a$)$ Derive the formula of the reaction at the support A in terms of angle $.[7$ PTS$]$

$($b$)$ For angle $=30,$ determine the reaction at the support A$.[3$ PTS$]$

$($c$)$ For angle $=75,$ determine the reaction at the support A $.$ What is your assessment regarding the stability of this object $[$Extra $3$ PTS$]?$