\(\vec{\ \ F2x}=-2mg\cos\ 80\)
\(=-2\ mg\ sen\ 10\)
\(\vec{\ \ \ F2y}=2\ mg\ \cos10\)
\(=2\ mg\ sen\ 80\)
\(\ \ \ \vec{F2}=-2mg\cos80°+2\ mg\ sen\ 80°\)
\(\ \ \ \vec{F1}=-2mg\cos40°+mg\ sen\ 40°\)
\(\ \ \vec{F1}+\vec{F2}=mg\left[\left(-0.347+0.766\right)i+\left(1.969+0.642\right)\right]j\)
\(\ \ \vec{F1}+\vec{\vec{F2}}=mg\left[0.419i+2.612\right]j\)
\(\tan^{-1}=\frac{2.612}{0.419}+80.90\)
\(\vec{\left|F1\right|}=2.645\ mg\)
\(\theta=\tan^{-1}\left(\frac{\vec{F1y}+\vec{F2}y}{\vec{F1}x+\vec{F2}x}\right)\)
\(\vec{F1}+\vec{F2}=2\ \cos100+\cos100+2\ sen\ 100+sen\ 100\)
\(\tan^{-1}=\frac{2.954}{-0.520}=-80.00\)