Answer
The magnitude of the second force is 93.9 lb
The magnitude of the resultant is 116.7 lb
Work Step by Step
Let $a = 28.7~lb$
Let $b$ be the second force.
Let $c$ be the resultant force.
When we use $a$ and $b$ to complete the parallelogram, the angles $A, B,$ and $C$ form a triangle, where $a$ is opposite angle $A$, $b$ is opposite angle $B$, and $c$ is opposite angle $C$.
Angle $B = 32^{\circ}40'$. Angle $A = 42^{\circ}10'-32^{\circ}40'$ which is $A = 9^{\circ}30'$
We can use the law of sines to find $b$:
$\frac{b}{sin~B} = \frac{a}{sin~A}$
$b = \frac{a~sin~B}{sin~A}$
$b = \frac{(28.7~lb)~sin~32^{\circ}40'}{sin~9^{\circ}30'}$
$b = 93.9~lb$
The magnitude of the second force is 93.9 lb
Angle $C = 180^{\circ}- 42^{\circ}10' = 137^{\circ}50'$
We can use the law of sines to find $c$, which is the resultant:
$\frac{c}{sin~C} = \frac{a}{sin~A}$
$c = \frac{a~sin~C}{sin~A}$
$c = \frac{(28.7~lb)~sin~137^{\circ}50'}{sin~9^{\circ}30'}$
$c = 116.7~lb$
The magnitude of the resultant is 116.7 lb