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)

Question

Responses

45°
45°

23°
23°

79°
79°

11°

Answer 1

To find the approximate angle formed between the sidewalk and the base of the ramp, we can use the tangent function in trigonometry, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.

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 \( \theta \) can be calculated as follows:

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

Now, we can use the inverse tangent function (also known as arctan or tan⁻¹) to find the angle \( \theta \):

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

Calculating this gives:

\[ \theta \approx 11.31° \]

So, the angle formed between the sidewalk and the base of the ramp is approximately 11°.

The correct response is:

11°