Question

an airplane wishes to fly directly EAST at 900km/h. however a wind is blowing from 65 degrees south of east at 80 what is the planes heading? give magnitude and direction

Answer 1

$$v=\sqrt{900^2+80^2-2(900)(80)\cos{65}}=869\frac{km}{h}$$

$$\theta=\arcsin{\left(\frac{80}{869}\sin{65}\right)}=4.8\degree\text{ N of E}$$