To find the angle of elevation from the base of the stairs to the bottom of the door using the inverse tangent function, we can use the formula:
\[ \theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]
In this case, the "opposite" side is the height from the garage floor to the bottom of the door, which is 3 feet. The "adjacent" side is the distance from the wall to the base of the stairs, which is 5 feet.
Substituting in the values, we get:
\[ \theta = \tan^{-1}\left(\frac{3}{5}\right) \]
Now we calculate:
\[ \theta = \tan^{-1}(0.6) \]
Using a calculator, we find that:
\[ \theta \approx 30.96 \text{ degrees} \]
Rounding this to the nearest whole degree:
\[ \theta \approx 31 \text{ degrees} \]
Thus, the angle of elevation from the base of the stairs to the bottom of the door is approximately 31 degrees.