$(30$ pt$)$ Three forces act on the bracket. Determine the magnitude and direction $$ of $F$ so that the resultant

force is directed along the positive $x^{\text{'}}$ axis and has a magnitude of $80$ N when $=10$ and $=25.($Figure $($a$)$ :

below left$)$

$($a$)$ Problem $1$

$(30$ pt$)$ Determine the angle between $AD$ and $AC.($Figure $($b$)$ : above right$)$

$(40$ pt$)$ Determine the magnitudes of the components of $F=80N$ acting along and perpendicular to segment

$AB$ of the pipe assembly.