To find the angle of elevation of the ramp, we can use the tangent function in trigonometry, which is defined as:
\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \]
In this scenario:
- The "opposite" side is the height of the ramp from the ground to the doorway, which is 1 foot.
- The "adjacent" side is the horizontal distance from the bottom of the ramp to the building, which is 10 feet.
We can set up the equation as follows:
\[ \tan(\theta) = \frac{1}{10} \]
To find the angle \(\theta\), we take the arctangent (inverse tangent) of both sides:
\[ \theta = \tan^{-1}\left(\frac{1}{10}\right) \]
Now calculating this value:
\[ \theta \approx \tan^{-1}(0.1) \]
Using a calculator to find the arctangent:
\[ \theta \approx 5.71^\circ \]
Rounding to the nearest degree:
\[ \theta \approx 6^\circ \]
Therefore, the angle of elevation of the ramp to the nearest degree is \( \boxed{6} \).
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