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°.