Question

Tammy is an electrician. When using a ladder, her company requires the angle formed between the ground and the ladder to be within 3 degrees of 75 degrees so that she remains safe. if she is using a 20-foot ladder and placed the ladder 5 feet from the wall, is this within safety protocol? what is the approximate angle formed between the ground and the ladder?
A. no, the angle formed is approximately 14 degrees
B. yes the angle formed is approximately 73 degrees
C. Yes, the angle formed is approximately 76 degrees
D. no the angle formed is approximately 90 degrees

Answer 1

To find the angle formed between the ground and the ladder, we can use trigonometry. Specifically, we can use the sine function, which relates the opposite side over the hypotenuse in a right triangle.

First, we have the following:

- Length of the ladder (hypotenuse) = 20 feet
- Distance from the wall (adjacent side) = 5 feet

We will use the cosine function, given by:

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

Substituting in the known values:

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

Now, we find the angle \( \theta \) by taking the inverse cosine:

\[
\theta = \cos^{-1}(0.25)
\]

Using a calculator:

\[
\theta \approx 75.5 \text{ degrees}
\]

Now we can check if this angle is within the safety protocol, which states that the angle must be within 3 degrees of 75 degrees. So, the acceptable range is:

- Minimum angle = 75 - 3 = 72 degrees
- Maximum angle = 75 + 3 = 78 degrees

Since \( 75.5 \) degrees is within the range of 72 to 78 degrees, the angle is considered safe.

Thus, the correct answer is **C. Yes, the angle formed is approximately 76 degrees.**