To find the angle formed between the sidewalk and the base of the ramp, we can use the tangent function from trigonometry. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
In this case:
- The height of the blocks (opposite side) is 1 foot.
- The distance from the base of the blocks to where the wood plank touches the sidewalk (adjacent side) is 5 feet.
We can use the formula:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{1 \text{ ft}}{5 \text{ ft}} = \frac{1}{5} \]
To find the angle \( \theta \), we take the arctangent (inverse tangent) of \( \frac{1}{5} \):
\[ \theta = \tan^{-1}\left(\frac{1}{5}\right) \]
Using a calculator or trigonometric table,
\[ \theta \approx 11.31^\circ \]
Therefore, the approximate angle formed between the sidewalk and the base of the ramp is about 11°.
So the correct response is:
11°