Answer
$F = 1 230 N$
$\theta = 6.08°$
Work Step by Step
We are given both the direction and magnitude of both F1 and F2 and are asked for the magnitude and direction of F (the sum of both forces).
By projecting the forces on the x axis
$F_{x} = 750 \times \sin(45°) + 800 \times \cos(30°) = 1 223.15 N$
By projecting the forces on the y axis
$F_{y} = 750 \times \cos(45°) - 800 \times \sin(30°) = 130.33 N$
The magnitude of F is obtained
$F = \sqrt (F_{x}^{2} + F_{y}^{2}) = 1230 N$
The angle from the x axis is obtained
$\theta = \tan^{-1} (\frac{F_{x}}{F_{y}}) = 6.08°$
