HW$2\mathrm{.}6.$ Particle $-$ Spring and cable

A cable and a spring are connected together at point $B$ and held in equilibrium by a vertical force $F,$ as

shown in the figure below. The cable has a length $L_{AB}=4ft$ and is oriented at an angle $=55$ from the

horizontal, and the spring has a spring constant $k=65l\frac{b}{f}t.$ Note that the cable and unstretched spring

were initially aligned horizontally between points A and $C$ before loading, with a combined length of

$L_w=9ft.$ Determine the force in the spring $(F_{BC})$ and the applied force $F.$