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?
22.1 degrees
20.6 degrees
69.4 degrees
67.9 degrees
22.1 degrees
20.6 degrees
69.4 degrees
67.9 degrees
Answers
GPT-4o mini
To find the angle formed where the ladder rests on the wall, we can use the tangent function. The slope is given as 8/3, which represents the ratio of the height of the wall (opposite side) to the base (adjacent side) of the triangle formed by the ladder against the wall.
The angle \( \theta \) can be calculated using the inverse tangent (arctan) function:
\[
\theta = \tan^{-1}\left(\frac{8}{3}\right)
\]
Now, we can compute this:
\[
\theta \approx \tan^{-1}\left(2.6667\right)
\]
Using a calculator:
\[
\theta \approx 69.4 \text{ degrees}
\]
So, the angle formed where the ladder rests on the wall is approximately **69.4 degrees**.
The angle \( \theta \) can be calculated using the inverse tangent (arctan) function:
\[
\theta = \tan^{-1}\left(\frac{8}{3}\right)
\]
Now, we can compute this:
\[
\theta \approx \tan^{-1}\left(2.6667\right)
\]
Using a calculator:
\[
\theta \approx 69.4 \text{ degrees}
\]
So, the angle formed where the ladder rests on the wall is approximately **69.4 degrees**.