To calculate the angle of elevation formed between the board and the lower side of the ditch, we can use trigonometry.
Given:
- The length of the board (hypotenuse) \( L = 8 \) ft.
- The height difference (opposite side) \( h = 3 \) ft.
We can use the sine function to find the angle of elevation \( \theta \):
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L} = \frac{3}{8} \]
To find \( \theta \), we take the inverse sine:
\[ \theta = \sin^{-1}\left(\frac{3}{8}\right) \]
Now, we calculate \( \sin^{-1}(3/8) \).
Calculating \( \frac{3}{8} = 0.375 \).
Now we will use a calculator to find \( \theta \):
\[ \theta \approx \sin^{-1}(0.375) \approx 22.03^\circ \]
Rounding to the nearest whole number:
\[ \theta \approx 22^\circ \]
Thus, the approximate angle of elevation formed between the board and the lower side of the ditch is \( \boxed{22} \).