If the height of a tower and the distance of the point of observation from its foot are both increased by 10%, then the angle of elevation of the top…

Let the initial height be $h$ and the initial distance be $x$. The angle of elevation $\theta$ is given by $\tan \theta = \frac{h}{x}$. When both are increased by 10%, the new height is $1.1h$ and the new distance is $1.1x$. The new angle $\theta'$ satisfies $\tan \theta' = \frac{1.1h}{1.1x} = \frac{h}{x} = \tan \theta$. Therefore, the angle remains unchanged.