Question

Dedrea is making a bike ramp on the sidewalk in front of their house. They place a wood plank on top of blocks to form the ramp. The blocks are one foot in height, and the distance from the base of the blocks to where the wood plank touches the sidewalk is five feet.
What is the approximate angle formed between the sidewalk and the base of the ramp? (1 point)
0 79°
011°
• 45°
0 23°

Answer 1

To determine the angle formed between the sidewalk and the base of the ramp, we can use trigonometry. Specifically, we will use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.

In this case:
- The height of the ramp (opposite side) is 1 foot (the height of the blocks).
- The distance from the blocks to the point where the plank touches the sidewalk (adjacent side) is 5 feet.

Using the tangent function:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{5}
\]

Now, we can find the angle \(\theta\) by taking the arctangent (inverse tangent) of \(\frac{1}{5}\):

\[
\theta = \tan^{-1}\left(\frac{1}{5}\right)
\]

Using a calculator to find this value:

\[
\theta \approx \tan^{-1}(0.2) \approx 11.3°
\]

Rounding this to the nearest whole number, we get approximately 11°.

Therefore, the correct answer is **11°**.