In the figure, $\varphi$ represents the angle subtended by a 5 ft picture when viewed from point P that is 7 ft below the picture and 14 ft away from the wall on which the picture hangs.

$\tan \theta = 7/14$
 

$\tan (\theta + \varphi) = 12/14$

$\dfrac{\tan \theta + \tan \varphi}{1 - \tan \theta \, \tan \varphi} = \dfrac{12}{14}$

$\dfrac{\frac{7}{14} + \tan \varphi}{1 - \frac{7}{14} \tan \varphi} = \dfrac{12}{14}$

$7 + 14 \tan \varphi = 12 - 6 \tan \varphi$

$20 \tan \varphi = 5$

$\tan \varphi = 5/20$

$\varphi = \arctan (1/4)$