To determine if Tammy's ladder placement is within the safety protocol, we first need to calculate the angle formed by the ladder with the ground when it is leaning against the wall.
We can use trigonometry here. Specifically, we will use the cosine function, which relates the angle to the lengths of the adjacent side (ground distance from the wall) and the hypotenuse (length of the ladder).
Let:
- \( L \) = length of the ladder = 20 feet
- \( d \) = distance from the wall = 5 feet
- \( \theta \) = angle between the ground and the ladder
The cosine of the angle is given by:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{d}{L} \]
Substituting the known values:
\[ \cos(\theta) = \frac{5}{20} = 0.25 \]
Next, we calculate \( \theta \) by taking the inverse cosine (also called arccos):
\[ \theta = \cos^{-1}(0.25) \]
Calculating \( \theta \):
\[ \theta \approx 75.52° \]
Now we check if this angle is within the safety protocol. The company's requirement states that the angle must be within 3° of 75°. This means the acceptable range of angles is:
- Lower limit: \( 75° - 3° = 72° \)
- Upper limit: \( 75° + 3° = 78° \)
So, the acceptable angle range is from 72° to 78°.
Since \( \theta \approx 75.52° \), we find:
\[ 72° \leq 75.52° \leq 78° \]
This means that the angle is indeed within the safety protocol. Therefore, Tammy's ladder positioning is safe.
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