Answer:
[tex]F=16.512\ N[/tex]
[tex]\theta=74.38^{\circ}[/tex]
Explanation:
Given:
Observe the schematic showing the angle direction and magnitude of the forces acting on the center of the mass.
Here we find that there are 3 forces acting on a point and we can build a relation among the forces and the angle between them using Lami's Theorem.
[tex]\frac{8.1}{sin\ (134-\theta)} =\frac{F}{sin\ (136)} =\frac{6.4}{sin\ (90+\theta)}[/tex]
Now, from the extreme left and extreme right term:
[tex]\frac{8.1}{sin\ (134-\theta)} =\frac{6.4}{sin\ (90+\theta)}[/tex]
[tex]\frac{8.1}{6.4} \times cos\ \theta=0.72\times cos\ \theta+0.7\times sin\ \theta[/tex]
[tex]\theta=74.12^{\circ}[/tex]
Now, for calculating force F:
[tex]\frac{F}{sin\ (136)} =\frac{6.4}{sin\ (74.12+\theta)}[/tex]
[tex]F=16.25\ N[/tex]
