Tammy is an electrician. When using a ladder, her company requires the angle formed between the ground and the ladder to be within 3° of 75° so that she remains safe. If she is using a 20-foot ladder and places the ladder 5 feet from the wall, is this within safety protocol?

To determine the angle formed between the ladder and the ground, we can use trigonometry. We will use the sine function, which relates the opposite side (the height of the wall the ladder reaches) to the hypotenuse (the length of the ladder). However, we need the cosine function since we know the base (distance from the wall to the ladder's base) and the hypotenuse.

The cosine of the angle (θ) can be found using the formula:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

In this case:

• The adjacent side (distance from the wall) = 5 feet
• The hypotenuse (length of the ladder) = 20 feet

So:

\[ \cos(\theta) = \frac{5}{20} = 0.25 \]

Now, we can find the angle θ by taking the arccosine (inverse cosine):

\[ \theta = \arccos(0.25) \]

Calculating this gives:

\[ \theta \approx 75.52° \]

Now, we need to check if this angle is within the required range. The acceptable range is from 72° to 78° (75° ± 3°).

Since 75.52° is within this range, we can conclude:

Yes, the angle formed is approximately 76°. (This is the closest answer choice given the options you provided.)