An aircraft is travelling at an angle $\theta$ east of north, with a horizontal velocity relative to the air of $800 \, \text{km h}^{-1}$. A wind is blowing horizontally from east to west at $200 \, \text{km h}^{-1}$, as illustrated. The aircraft's resultant velocity is directed due north. Find the value of angle $\theta$ and the size of the resultant velocity.
Physics 9702 · AS & A Level · Scalars and vectors