The speed of a swimmer in still water is $20\text{m/s}$. The speed of river water is $10\text{m/s}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his strokes w.r.t. north is given by:

To cross via the shortest path (directly across to the north), the resultant velocity must be directed North.Let the swimmer's velocity relative to water be ${\vec{V}}_{sw}$ at an angle $\theta$ west of north.The component of swimmer's velocity along the river must cancel the river's flow ($V_r=10\text{m/s}$ east).
$$V_{sw}\sin \theta =V_r$$
$$20\sin \theta =10$$
$$\sin \theta =0.5⟹\theta =30^{\circ }$$
So the swimmer should aim $30^{\circ }$ west of north.