Chapter 7 - Applications of Trigonometry and Vectors - Section 7.4 Vectors, Operations, and the Dot Product - 7.4 Exercises - Page 330: 51

The magnitude of the resultant force is 88.2 lb

Let $a = 116~lb$ Let $b = 139~lb$ Let angle $\theta = 140^{\circ}50' = 140.83^{\circ}$ We can use the parallelogram rule to find $c$, the magnitude of the resultant force: $c = \sqrt{a^2+b^2+2ab~cos~\theta}$ $c = \sqrt{(116~lb)^2+(139~lb)^2+(2)(116~lb)(139~lb)~cos~140.83^{\circ}}$ $c = \sqrt{7775.92~lb^2}$ $c = 88.2~lb$ The magnitude of the resultant force is 88.2 lb