(Solved): Question: Where did the highlighted angle come from. Please show all math 3-5. A sign is subjected ...

Question: Where did the highlighted angle come from. Please show all math

3-5. A sign is subjected to a wind loading that exerts horizontal forces of \( 300 \mathrm{lb} \) on joints \( B \) and \( C \) of one of the side supporting trusses. Determine the force in each member of the truss and state if the members are in tension or compression. Joint \( C: \) Fig \( a \). \[ \begin{array}{l} \stackrel{+}{\rightarrow} \sum F_{x}=0 ; \quad 300-F_{C D}\left(\frac{5}{13}\right)=0 \quad F_{C D}=780 \mathrm{lb}(\mathrm{C}) \\ +\uparrow \sum F_{y}=0 ; \quad 780\left(\frac{12}{13}\right)-F_{C B}=0 \quad F_{C B}=720 \mathrm{lb}(\mathrm{T}) \end{array} \] Joint \( D \) : Fig. \( b \). \[ \begin{array}{ll} +\nearrow \sum F_{x}=0 ; & F_{D B}=0 \\ +\nwarrow \sum F_{y}=0 ; & F_{D E}-780=0 \quad F_{D E}=780 \mathrm{lb}(\mathrm{C}) \end{array} \] Joint \( B: \) Fig. \( c \). \[ \begin{array}{ll} \stackrel{+}{\rightarrow} \sum F_{x}=0 ; & 300+F_{B E} \sin 45.24^{\circ}-F_{B A} \cos 45^{\circ}=0 \\ +\uparrow \sum F_{y}=0 ; & 720-F_{B E} \cos 45.24^{\circ}-F_{B A} \sin 45^{\circ}=0 \end{array} \] Solving \[ F_{B E}=296.99 \mathrm{lb}=297 \mathrm{lb}(\mathrm{T}) \quad F_{B A}=722.49 \mathrm{lb}(\mathrm{T})=722 \mathrm{lb}(\mathrm{T}) \]