Answer
The angle between the forces is $70.1^{\circ}$
Work Step by Step
Let $a = 128~lb$
Let $b = 253~lb$
Let $c$ be the resultant force of $320~lb$
Let $\theta$ be the angle between $a$ and $b$
We can use the parallelogram rule to find $\theta$:
$c^2 = a^2+b^2+2ab~cos~\theta$
$-2ab~cos~\theta = a^2+b^2-c^2$
$cos~\theta = -\frac{a^2+b^2-c^2}{2ab}$
$\theta = arccos(-\frac{a^2+b^2-c^2}{2ab})$
$\theta = arccos(-\frac{128^2+253^2-320^2}{(2)(128)(253)})$
$\theta = arccos(0.33978)$
$\theta = 70.1^{\circ}$
The angle between the forces is $70.1^{\circ}$
