Question

a 78 kg object experiences the following forces:
65 N [w], 72 N [NW], 87 N [E30S]
find the net force acting on it.

Answer 1

$$F=(-65,0)+(-72\cos{45},72\sin{45})+\\+(87\sin{45},-87\cos{45})$$

$$F=(-54.4,-10.6)N$$

$$F=\sqrt{54.4^2+10.6^2}=55.4\ N$$

$$\theta=\arctan{\frac{10.6}{55.4}}=10.8\degree\text{S of W}$$