To find the angle of elevation of the ramp, you can use trigonometry. Specifically, the tangent of the angle of elevation (θ) can be represented by the ratio of the opposite side (the height of the ramp) to the adjacent side (the horizontal distance from the base of the ramp to the building).
In this problem:
- The height of the ramp (opposite side) is 1 foot.
- The distance along the ramp (hypotenuse) is 5 feet.
To find the horizontal distance (adjacent side), we can apply the Pythagorean theorem:
\[ \text{hypotenuse}^2 = \text{opposite}^2 + \text{adjacent}^2 \]
Let the horizontal distance be \( x \). Then:
\[ 5^2 = 1^2 + x^2 \]
Calculating the squares:
\[ 25 = 1 + x^2 \]
Subtracting 1 from both sides:
\[ 24 = x^2 \]
Taking the square root of both sides:
\[ x = \sqrt{24} \approx 4.899 \]
Now we can find the angle of elevation using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{\sqrt{24}} \]
Now we can convert this to a degree measure using the arctangent function:
\[ \theta = \tan^{-1}\left(\frac{1}{\sqrt{24}}\right) \]
Calculating this approximately:
\[ \frac{1}{\sqrt{24}} \approx \frac{1}{4.899} \approx 0.2041 \] \[ \theta \approx \tan^{-1}(0.2041) \approx 11.54^{\circ} \]
Rounding to the nearest degree:
\[ \theta \approx 12^{\circ} \]
Thus, the angle of elevation of the ramp is approximately 12 degrees.