To find the angle formed between the ground and the ladder, we can use trigonometry. Specifically, we can use the cosine function since we have the adjacent side (the distance from the wall) and the hypotenuse (the length of the ladder).
Given:
- Length of the ladder (hypotenuse) = 20 feet
- Distance from the wall (adjacent side) = 5 feet
We can find the angle \(\theta\) using the formula:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{5}{20} = 0.25 \]
Now, we calculate \(\theta\):
\[ \theta = \cos^{-1}(0.25) \]
Using a calculator,
\[ \theta \approx 75.5° \]
Now, we must check if this angle is within 3° of 75°:
- Lower limit: \(75° - 3° = 72°\)
- Upper limit: \(75° + 3° = 78°\)
Since \(75.5°\) falls between \(72°\) and \(78°\), the angle is indeed within the safety protocol.
Thus, the closest response is:
Yes, the angle formed is approximately 76°.
1 answer