Question
A ladder leaning against a wall creates a slope of 8/3
. Using the inverse of tangent, what is the angle formed where the ladder rests on the wall?(1 point) 8 is the adjacent and 3 is the opposite
Responses
67.9°
67.9 degrees
20.6°
20.6 degrees
69.4°
69.4 degrees
22.1°
22.1 degrees
. Using the inverse of tangent, what is the angle formed where the ladder rests on the wall?(1 point) 8 is the adjacent and 3 is the opposite
Responses
67.9°
67.9 degrees
20.6°
20.6 degrees
69.4°
69.4 degrees
22.1°
22.1 degrees
Answers
GPT-4o mini
To find the angle formed where the ladder rests on the wall, we can use the inverse tangent function.
Given that the slope is \( \frac{8}{3} \), where:
- The adjacent side (base) is 8
- The opposite side (height) is 3
We can use the following formula:
\[
\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) = \tan^{-1}\left(\frac{3}{8}\right)
\]
Calculating this:
\[
\theta = \tan^{-1}\left(\frac{3}{8}\right)
\]
Using a calculator:
\[
\theta \approx 20.6°
\]
So, the angle formed where the ladder rests on the wall is approximately **20.6 degrees**.
Thus, the correct response is:
**20.6°**
Given that the slope is \( \frac{8}{3} \), where:
- The adjacent side (base) is 8
- The opposite side (height) is 3
We can use the following formula:
\[
\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right) = \tan^{-1}\left(\frac{3}{8}\right)
\]
Calculating this:
\[
\theta = \tan^{-1}\left(\frac{3}{8}\right)
\]
Using a calculator:
\[
\theta \approx 20.6°
\]
So, the angle formed where the ladder rests on the wall is approximately **20.6 degrees**.
Thus, the correct response is:
**20.6°**