$P_x = 722(\frac{2}{\sqrt{13}}) = 400.49 \, \text{ lb}$
$P_y = 722(\frac{3}{\sqrt{13}}) = 600.74 \, \text{ lb}$
$Q_x = -200 \cos 60^\circ = -100 \, \text{ lb}$
$Q_y = 200 \sin 60^\circ = 173.20 \, \text{ lb}$
$F_x = -448(\frac{2}{\sqrt{5}}) = -400.70 \, \text{ lb}$
$F_y = -448(\frac{1}{\sqrt{5}}) = -200.35 \, \text{ lb}$
$T_x = 400 \sin 20^\circ = 136.81 \, \text{ lb}$
$T_y = -400 \cos 20^\circ = -375.88 \, \text{ lb}$
Rectangular Representation
${\bf F} = F (\cos \theta_x {\bf i} + \sin \theta_x {\bf j})$
${\bf P} = 722 (\frac{2}{\sqrt{13}} {\bf i} + \frac{3}{\sqrt{13}} {\bf j}) = 400.49 {\bf i} + 600.74 {\bf j} \, \text{ lb}$
${\bf Q} = 200 (-\cos 60^\circ {\bf i} + \sin 60^\circ {\bf j}) = -100 {\bf i} + 173.20 {\bf j} \, \text{ lb}$
${\bf F} = 448 (-\frac{2}{\sqrt{5}} {\bf i} - \frac{1}{\sqrt{5}} {\bf j}) = -400.70 {\bf i} - 200.35 {\bf j} \, \text{ lb}$
${\bf T} = 400 (\sin 20^\circ {\bf i} - \cos 20^\circ {\bf j}) = 136.81 {\bf i} - 375.88 {\bf j} \, \text{ lb}$
The coefficients of i and j from the vector notations are the respective x and y components of each force.
Calculator Techniques
