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? What is the approximate angle formed between the ground and the ladder?(1 point)

Responses

No, the angle formed is approximately 90°.
No, the angle formed is approximately 90°.

Yes, the angle formed is approximately 76°.
Yes, the angle formed is approximately 76°.

No, the angle formed is approximately 14°.
No, the angle formed is approximately 14°.

Yes, the angle formed is approximately 73°.
Yes, the angle formed is approximately 73°.

1 answer

To find the angle formed between the ground and the ladder, we can use trigonometry. We have a ladder (hypotenuse) of 20 feet and the distance from the wall (adjacent side) of 5 feet. We will use the cosine function, which is defined as:

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

Plugging in the values:

\[ \cos(\theta) = \frac{5}{20} = \frac{1}{4} \]

Now, to find the angle \(\theta\), we need to take the arccosine (inverse cosine) of \( \frac{1}{4} \):

\[ \theta = \arccos\left(\frac{1}{4}\right) \]

Calculating this gives us:

\[ \theta \approx 75.5° \]

This angle is within the safety protocol of being within 3° of 75°, as it falls between 72° and 78°.

Thus, the correct response is:

Yes, the angle formed is approximately 76°.