Chapter 7 - Applications of Trigonometry and Vectors - Section 7.4 Vectors, Operations, and the Dot Product - 7.4 Exercises - Page 330: 50

The magnitude of the resultant force is 28.5 N

Let $a = 19~N$ Let $b = 32~N$ Let angle $\theta = 118^{\circ}$ We can use the parallelogram rule to find $c$, the magnitude of the resultant force: $c = \sqrt{a^2+b^2+2ab~cos~\theta}$ $c = \sqrt{(19~N)^2+(32~N)^2+(2)(19~N)(32~N)~cos~118^{\circ}}$ $c = \sqrt{814.12~N^2}$ $c = 28.5~N$ The magnitude of the resultant force is 28.5 N