Ellie is making a bike ramp. She places a wood plank on top of blocks to form the ramp. The blocks are 3 feet in height, and the distance from the base of the blocks to where the wood plank touches the sidewalk is 8 feet. What is the approximate angle formed between the base of the ramp and the sidewalk?(1 point)

Question

Responses

21°
21°

25°
25°

75°
75°

68°

Answer 1

To find the angle formed between the base of the ramp (the horizontal line from the base of the blocks to where the ramp touches the sidewalk) and the sidewalk, we can use the tangent function in trigonometry.

Given:

• Height of the blocks (opposite side) = 3 feet
• Horizontal distance from the base of the blocks to the sidewalk (adjacent side) = 8 feet

We can use the formula for the tangent of the angle $\theta$:

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

Substituting the values:

$$\tan (\theta )=\frac{3}{8}$$

Now, we'll calculate $\theta$ by taking the arctangent (inverse tangent) of $\frac{3}{8}$:

$$\theta ={\tan }^{-1}\left(\frac{3}{8}\right)$$

Using a calculator to find ${\tan }^{-1}(0.375)$:

$$\theta \approx 21°$$

Thus, the angle formed between the base of the ramp and the sidewalk is approximately 21°.

The correct response is: 21°.