Problem #$4-$ Concurrent Force System $(3$ parts, $20$ total points$)$

Three concurrent forces are acting at point $A$ in the figure below and are in a state of equilibrium.

Force $F_1$ has direction of $47\mathrm{.}6$ with the horizontal, force $F_2$ has magnitude of $12\mathrm{.}4kN$ and direction

of vertically upward, and force $F_3$ has direction of $57\mathrm{.}9$ with the horizontal axis as shown below.

Utilizing the method of rectangular components, determine the following:

A$.$ Draw the free$-$body diagram of $F_1$ and $F_3.$ Determine the rectangular components of these

forces. $(5$ points$)$

B$.$ Write the equilibrium equations that will be utilized to solve this diagram $($i$.$e$.,F_x,$ and

points