Chapter 7 - Applications of Trigonometry and Vectors - Section 7.4 Vectors, Operations, and the Dot Product - 7.4 Exercises - Page 330: 54

The magnitude of the resultant force is 158.0 lb

Let $a = 85~lb$ Let $b = 102~lb$ Let angle $\theta = 65^{\circ}$ We can use the parallelogram rule to find $c$, the magnitude of the resultant force: $c = \sqrt{a^2+b^2+2ab~cos~\theta}$ $c = \sqrt{(85~lb)^2+(102~lb)^2+(2)(85~lb)(102~lb)~cos~65^{\circ}}$ $c = \sqrt{24957.2~lb^2}$ $c = 158.0~lb$ The magnitude of the resultant force is 158.0 lb