Answer
See work. The forces must be added as vectors. The magnitude of the resultant force is less than the sum of the magnitudes of the individual forces, and depends on the angle between them.
Work Step by Step
a. Find the x-components of the forces.
$F_{1,x}=985 N cos 31^{\circ}=844.3N$
$F_{2,x}=788 N cos 122^{\circ} = -417.6N$
$F_{3,x}=411 N cos 233^{\circ} = -247.3N$
Add them to find the x-component of the sum.
$F_{sum,x}=179.39N$
Find the y-components of the forces.
$F_{1,y}=985 N sin 31^{\circ}=507.3N$
$F_{2,y}=788 N sin 122^{\circ} = 668.3N$
$F_{3,y}=411 N sin 233^{\circ} = -328.2N$
Add them to find the y-component of the sum.
$F_{sum,y}=847.34N$
b. Find the resultant force magnitude by using the Pythagorean Theorem.
$F=\sqrt{179.39^2+847.34^2}N=866N$
Find the resultant force’s angle by using trigonometry.
$\theta=tan^{-1}(\frac{847.34N}{179.39N})=78.1^{\circ}$
