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)

Responses

45°
45°

11°
11°

79°
79°

23°
23°

1 answer

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

In this case:

  • The height of the blocks (opposite side) is 1 foot.
  • The distance from the base of the blocks to where the wood plank touches the sidewalk (adjacent side) is 5 feet.

We can use the formula:

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

To find the angle \( \theta \), we take the arctangent (inverse tangent) of \( \frac{1}{5} \):

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

Using a calculator or trigonometric table,

\[ \theta \approx 11.31^\circ \]

Therefore, the approximate angle formed between the sidewalk and the base of the ramp is about 11°.

So the correct response is:

11°