To find the angle formed between the sidewalk and the base of the ramp, we can use the tangent function in trigonometry, which relates the opposite side to the adjacent side of a right triangle.
In this case:
- The height of the blocks (opposite side) = 1 foot
- The distance from the base of the blocks to where the wood plank touches the sidewalk (adjacent side) = 5 feet
The tangent of the angle (θ) is given by:
\[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{5} \]
Now we can find the angle by taking the arctangent (inverse tangent) of that ratio:
\[ θ = \tan^{-1}\left(\frac{1}{5}\right) \]
Using a calculator:
\[ θ \approx \tan^{-1}(0.2) \approx 11.31° \]
Therefore, the approximate angle formed between the sidewalk and the base of the ramp is 11°.
The correct response is:
11°