Part B: $(10$ points each, $30$ points total$)$:

Cat Burglars! Taco and Bubsy want to play video games too and are trying to steal my controller! Taco is pulling on the controller with a force of $10\mathrm{.}0$ N at an angle of $15\mathrm{.}0$ and Lucy is pulling on the controller with a force $15\mathrm{.}0$ N at an angle of $80\mathrm{.}0.$

a$)$ How much force $($magnitude$)$ do I need to apply to keep the controller from moving $($equilibrium$)?$

b$)$ At which angle $($direction$)$ do I need to apply this force? $($Think carefully about this!$)$