(Solved): A simple truss supports a force \( F \) at joint \( \mathrm{A} \), as shown in the figure below ...

A simple truss supports a force \( F \) at joint \( \mathrm{A} \), as shown in the figure below. The force has a magnitude \( F \) and is inclined by an angle \( \theta=75^{\circ} \) from the horizontal. The lengths for all horizontal members is \( s=7 \mathrm{~m} \) and for all vertical members is \( h=2 \mathrm{~m} \). The truss is held in equilibrium by a pin at point \( \mathrm{E} \) and a roller at point \( \mathrm{F} \). Using the method of joints, determine the largest applied force \( F_{\max } \) so that the force in each truss member does not exceed \( \pm 1300 \mathrm{kN} \). Note: Express tension forces as positive \( (+) \) and compression forces as negative \( (-) \).