To find the angle formed between the base of the ramp (the horizontal line from the base of the blocks to where the ramp touches the sidewalk) and the sidewalk, we can use the tangent function in trigonometry.
Given:
- Height of the blocks (opposite side) = 3 feet
- Horizontal distance from the base of the blocks to the sidewalk (adjacent side) = 8 feet
We can use the formula for the tangent of the angle \( \theta \):
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Substituting the values:
\[ \tan(\theta) = \frac{3}{8} \]
Now, we'll calculate \( \theta \) by taking the arctangent (inverse tangent) of \( \frac{3}{8} \):
\[ \theta = \tan^{-1}\left(\frac{3}{8}\right) \]
Using a calculator to find \( \tan^{-1}(0.375) \):
\[ \theta \approx 21° \]
Thus, the angle formed between the base of the ramp and the sidewalk is approximately 21°.
The correct response is: 21°.
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