Answer
$F_{R}=217N$
$\theta = 87°$
Work Step by Step
Projecting both forces on the x axis:
$F_{R}x = 200 \times \sin(45°) - 150 \times \cos (30°) = 11.518 N$
Projecting both forces on the y axis:
$F_{R} = 200 \times \cos(40°) + 150 \times \sin (30°) = 216.42N $
The magnitude of the force is obtained:
$F_{R} = \sqrt (11.518^{2} + 216.42^{2}) = 216.73 N \approx 217 N$
The direction relative to x axis is obtained:
$\theta = \tan^{-1} (\frac{F_{R}y}{F_{R}x}) = 86.95° \approx 87° $
