To find the angle formed between the base of the ramp and the sidewalk, we can use the tangent function from trigonometry. The tangent of an angle in a right triangle is given by the ratio of the opposite side to the adjacent side.
In this case:
- The height (opposite side) of the ramp is 3 feet (the height of the blocks).
- The distance (adjacent side) from the base of the blocks to where the wood plank touches the sidewalk is 8 feet.
We can set up the equation as follows:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{8} \]
To find the angle \(\theta\), we can take the arctangent (inverse tangent) of the ratio:
\[ \theta = \tan^{-1}\left(\frac{3}{8}\right) \]
Calculating this:
\[ \theta \approx \tan^{-1}(0.375) \]
Now you can use a calculator to find the arctangent:
\[ \theta \approx 20.6° \]
Rounding this to the nearest whole number gives approximately 21°.
The answer is:
21°