Rain is falling vertically with a speed of $35m{s}^{-1}$. Winds starts blowing after sometime with a speed of $12m{s}^{-1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

The velocity of the rain and the wind are represented by the vectors ${\overrightarrow{v}}_r$ and ${\overrightarrow{v}}_w$ as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity ${\overrightarrow{v}}_R$. If $\theta$ is the angle which resultant velocity ${\overrightarrow{v}}_R$ makes with the vertical, then $\tan \theta =\frac{v_w}{v_r}=\frac{12}{35}$  or $\theta ={\tan }^{-1}\left(\frac{12}{35}\right)$