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) Responses 45° 45° 79° 79° 23° 23° 11°

Answer 1

To find the angle formed between the sidewalk and the base of the ramp, we can use the tangent function in trigonometry.

The ramp forms a right triangle where:

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

We can use the tangent function, which is defined as:

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

So:

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

To find the angle \(\theta\), we take the arctangent (inverse tangent):

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

Calculating this:

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

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

The correct response is 11°.