Question Find the magnitude of a force pulling $45.8^{\circ}$ west and the direction of the $166.2 \mathrm{N}$ resultant force when a $116 \mathrm{N}$ force pulls due west.

Studdy Solution
Now we have all the information to write the final answer. Calculate the exact values of $|F_2|$ and $\theta$ using the equations derived in previous steps.
$$\left|F_{2}\right|=\frac{-(2 \cdot 116 \mathrm{~N} \cdot \cos(45.8^{\circ})) + \sqrt{\Delta}}{2} \mathrm{~N}$$
$$\theta = \left|\arctan\left(\frac{|F_2| \sin(45.8^{\circ})}{-116 \mathrm{~N} - |F_2| \cos(45.8^{\circ})}\right)\right|^{\circ}$$
The magnitude of the second force is $\left|F_{2}\right|$ N, and the direction of the resultant is $\mathrm{N}\theta^{\circ} \mathrm{W}$.