To determine the angle formed between the ground and the ladder, we can use trigonometry. Specifically, we can use the cosine function, which relates the angle \(\theta\) to the lengths of the adjacent side (distance from the wall) and the hypotenuse (length of the ladder).
We have:
- Length of the ladder (hypotenuse) = 20 feet
- Distance from the wall (adjacent side) = 5 feet
We can find the angle using the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{5}{20} = 0.25 \]
Next, we calculate the angle \(\theta\):
\[ \theta = \cos^{-1}(0.25) \]
Using a calculator:
\(\theta \approx 75.5°\)
Now, we need to check if this angle is within the company's safety protocol, which allows for an angle within 3° of 75°. This means the acceptable angle range is:
\[ 75° - 3° = 72° \quad \text{to} \quad 75° + 3° = 78° \]
Since \(75.5°\) falls within the range of \(72°\) to \(78°\), we can conclude that:
Yes, the angle formed is approximately 76°.
1 answer