The problem asks for the direction to hold the umbrella to protect against rain affected by wind. This is a problem of finding the direction of the resultant velocity of the rain and wind.

1. Identify Velocity Vectors: Velocity of rain, $\mathbf{v}_r = 35 \text{ m/s}$ (acting vertically downward) . Velocity of wind, $\mathbf{v}_w = 12 \text{ m/s}$ (acting horizontally from east to west) .

2. Determine Resultant Direction: The effective velocity of the rain relative to the stationary boy is the vector sum (resultant) of the rain's velocity and the wind's velocity: $\mathbf{R} = \mathbf{v}_r + \mathbf{v}_w$. The umbrella must be held along the line of this resultant velocity.

3. Calculate the Angle ($\theta$): Let $\theta$ be the angle the resultant makes with the vertical (the original direction of the rain). From the vector diagram (parallelogram law): $\tan \theta = \frac{v_w}{v_r}$ Substituting the given values: $\tan \theta = \frac{12}{35}$ $\theta = \tan^{-1}\left(\frac{12}{35}\right)$

Since the vertical direction corresponds to the initial direction of the rain, the angle is $\tan^{-1}\left(\frac{12}{35}\right)$ with respect to the rain .