Chapter 7 - Applications of Trigonometry and Vectors - Section 7.4 Vectors, Operations, and the Dot Product - 7.4 Exercises - Page 330: 52

The magnitude of the resultant force is 76.2 lb

Let $a = 37.8~lb$ Let $b = 53.7~lb$ Let angle $\theta = 68.5^{\circ}$ We can use the parallelogram rule to find $c$, the magnitude of the resultant force: $c = \sqrt{a^2+b^2+2ab~cos~\theta}$ $c = \sqrt{(37.8~lb)^2+(53.7~lb)^2+(2)(37.8~lb)(53.7~lb)~cos~68.5^{\circ}}$ $c = \sqrt{5800.422~lb^2}$ $c = 76.2~lb$ The magnitude of the resultant force is 76.2 lb