\(\cos\theta=\frac{4}{5}\)
\(\tan=\frac{3}{4}\)
\(FAX=FA\ \cos\theta=\frac{4}{5\ }FA\)
\(FAY=FA\ \sin\theta=\frac{3}{5}FA\)
\(FBX=FB\ \cos60\)
\(FBY=FB\ \sin60\)
\(\Sigma FX=0\)
\(-FBX-FAX=0\)
\(-30lb\ \cos\ 60-\frac{4}{5}FA=0\)
\(\frac{4}{5}FA=\ -30lb\ \cos\ 60\)
\(FA=\frac{4}{5}\left(-30lb\cos60\right)\)
\(FA=18.75\) Valor valido si las fuerzas estuvieran en el mismo punto.
Para B
\(rBx=6ft\ \ FBx=-30lb\cos60°\)
\(rBy=0\ \ \ \ FBy=30lb\sin60°\)
Para A
\(rAx=9ft\ \ \ FAx=\frac{4}{5}\ FA\)
\(rAy=0\ \ \ \ FAy=\frac{3}{5}FA\)
\(MA=rAx\ \ FAy-rAy\ FAx\)
\(=\left(9ft\right)\left(\frac{3}{5}\right)-\left(0\right)\left(\frac{4}{5}FA\right)\)
\(=\frac{27}{5}lb.ft\)
\(MB=rBx\ \ FBy-rBy\ \ FBx\)
\(=\left(6ft\right)\left(30lb\sin60°\right)-\left(0\right)\left(30lb\cos60°\right)\) \(=155.88lb.ft\)
\(\Sigma M=0\)\(MB-MA=0\)
\(155.88lb.ft-\frac{27}{5}lb.ft\)
\(\frac{27}{5}FA=155.88\)
\(FA=\frac{155.88}{\frac{27}{5}}\)
\(FA=28.86\)