Formulas:
\(\left|F_T\right|=\sqrt{\left(F_1X+F_2X\right)^2+\left(F_1Y+F_2Y\right)^2}\)
\(\theta=\tan^{-1}\left(\frac{F_1Y+F_2Y}{F_1X+F_2X}\right)\)
Datos:
\(F_1X=mg\cos45\)
\(F_2Y=mg\sin115\)
Solución:
\(=mg\cos\left(45\right)i+mg\sin\left(45\right)j\)
\(+mg\cos\left(115\right)i+mg\sin\left(115\right)j\)
\(=mg\left(\cos45+\cos115\right)i+mg\left(\sin45+\sin115j\right)\)
\(\left|F_T\right|=\sqrt{ }m^2g^2\left(\cos45+\cos115\right)^2+m^2g^2\left(\sin45+\sin115\right)^2\)
\(=mg\sqrt{\left(\cos45+2\cos115\right)^2+\left(\sin45+2\sin115\right)^2}\ =2.52\)
\(\theta=\tan^{-1}\left(\frac{\sin45+2\sin115}{\cos45+2\cos115}\right)=-86.86\)