Answer
The magnitude of the resultant force is 207.14 lb
Work Step by Step
Let $a = 100~lb$
Let $b = 130~lb$
The angle between $a$ and $b$ is $\theta = 52^{\circ}$
Then $C = 180^{\circ}-52^{\circ} = 128^{\circ}$
We can use the law of cosines to find $c$, which is the magnitude of the resultant force:
$c^2 = a^2+b^2-2ab~cos~C$
$c = \sqrt{a^2+b^2-2ab~cos~C}$
$c = \sqrt{(100~lb)^2+(130~lb)^2-(2)(100~lb)(130~lb)~cos~128^{\circ}}$
$c = \sqrt{42907.198~lb^2}$
$c = 207.14~lb$
The magnitude of the resultant force is 207.14 lb