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 73°. Yes, the angle formed is approximately 73°. No, the angle formed is approximately 14°. No, the angle formed is approximately 14°. Yes, the angle formed is approximately 76°.

1 answer

To determine the angle formed between the ground and Tammy's ladder using trigonometry, we can use the sine function or the tangent function.

Given:

  • Ladder length (hypotenuse) = 20 feet
  • Distance from the wall (adjacent side) = 5 feet

We can use the cosine function, which relates the adjacent side to the hypotenuse in a right triangle:

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

Now we will solve for the angle \(\theta\):

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

Calculating this, we find:

\[ \theta \approx 75.5^\circ \]

Since the acceptable range is within 3° of 75° (that is from 72° to 78°), 75.5° is within that range.

Therefore, the angle formed between the ground and the ladder is approximately 75.5°. The correct response is:

Yes, the angle formed is approximately 76°.