A banner 3 m tall hangs on a wall. Its lower edge is 2 m above the eye level of a visitor who…

Step 1. Two angles. At $4\ \text{m}$ the top edge is at $\tan^{-1}\dfrac{5}{4}$ and the lower edge is at $\tan^{-1}\dfrac{2}{4} = \tan^{-1}\dfrac{1}{2}$ above the horizontal.

Step 2. The difference. $xy = \dfrac{5}{4} \times \dfrac{1}{2} = \dfrac{5}{8} > -1$, so the angle is $\tan^{-1}\dfrac{\frac{5}{4} - \frac{1}{2}}{1 + \frac{5}{8}} = \tan^{-1}\dfrac{3/4}{13/8} = \tan^{-1}\dfrac{6}{13} = 0.4324$ radians, which is $24.78^\circ$.

Step 3. At $8\ \text{m}$. The two angles are $\tan^{-1}\dfrac{5}{8}$ and $\tan^{-1}\dfrac{1}{4}$. The difference is $0.5586 - 0.2450 = 0.3136$ radians.