To find the angle formed between the sidewalk and the base of the ramp, we can use the tangent function in trigonometry.
The ramp forms a right triangle where:
- The height of the blocks (opposite side) is 1 foot.
- The distance from the base of the blocks to where the plank touches the sidewalk (adjacent side) is 5 feet.
We can use the tangent function, which is defined as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
So:
\[ \tan(\theta) = \frac{1}{5} \]
To find the angle \(\theta\), we take the arctangent (inverse tangent):
\[ \theta = \tan^{-1}\left(\frac{1}{5}\right) \]
Calculating this:
\[ \theta \approx 11.31^\circ \]
Therefore, the angle formed between the sidewalk and the base of the ramp is approximately 11°.
The correct response is 11°.