#### Answer

The magnitude of the equilibrant force that Michael must apply is 30.4 lb.

#### Work Step by Step

Let $a = 15~lb$
Let $b = 20~lb$
Let angle $\theta = 25^{\circ}+35^{\circ} = 60^{\circ}$
We can use the parallelogram rule to find $c$, the magnitude of the resultant force:
$c = \sqrt{a^2+b^2+2ab~cos~\theta}$
$c = \sqrt{(15~lb)^2+(20~lb)^2+(2)(15~lb)(20~lb)~cos~60^{\circ}}$
$c = \sqrt{925~lb^2}$
$c = 30.4~lb$
The magnitude of the resultant force is 30.4 lb
The magnitude of the equilibrant force that Michael must apply is equal to the magnitude of the resultant force. Therefore, the magnitude of the equilibrant force that Michael must apply is 30.4 lb