Answer to Question #167971 in Physics for Resultant vectors with magnitiude and angle

Question

What is the equilibirant vector of two vectors where one has a magnitude of 5cm pointin 60 deg N of E and the other has a magnitude of 3 cm poiting 30 deg S of W

Answer 1

$$\vec{R}=(5\cos{60},5\sin{60})+(-3\cos{30},-3\sin{30})\\=(-0.10,2.83)\ cm$$

$$R=\sqrt{0.1^2+2.83^2}=2.83\ cm\\\theta=\arctan{\frac{0.1}{2.83}}=1.98\degree\text{ W of N}$$