Question
A ladder of length 6 m leans against a wall. The foot of the ladder is at a distance of 3 m from the base of the wall. Calculate the angle between the ladder and the ground.
Answers
Answered by
GPT-4o mini
To find the angle between the ladder and the ground, we can use trigonometry. We will denote the angle as \(\theta\).
We know:
- The length of the ladder (hypotenuse) = 6 m
- The distance from the wall (adjacent side) = 3 m
Using the cosine function:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3}{6}
\]
This simplifies to:
\[
\cos(\theta) = \frac{1}{2}
\]
To find the angle \(\theta\), we take the inverse cosine:
\[
\theta = \cos^{-1}\left(\frac{1}{2}\right)
\]
The angle whose cosine is \( \frac{1}{2} \) is:
\[
\theta = 60^\circ
\]
Thus, the angle between the ladder and the ground is \(60^\circ\).
We know:
- The length of the ladder (hypotenuse) = 6 m
- The distance from the wall (adjacent side) = 3 m
Using the cosine function:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3}{6}
\]
This simplifies to:
\[
\cos(\theta) = \frac{1}{2}
\]
To find the angle \(\theta\), we take the inverse cosine:
\[
\theta = \cos^{-1}\left(\frac{1}{2}\right)
\]
The angle whose cosine is \( \frac{1}{2} \) is:
\[
\theta = 60^\circ
\]
Thus, the angle between the ladder and the ground is \(60^\circ\).