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°.

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°.

Yes, the angle formed is approximately 76°.

To solve this, we need to calculate the angle formed between the ladder and the ground. Since we know the length of the ladder and the distance from the base of the ladder to the wall, we can use trigonometry to find the angle.

### Given:
- Ladder length (hypotenuse): \( 20 \) feet
- Distance from the base of the ladder to the wall (adjacent side): \( 5 \) feet

### Step 1: Use the cosine function
The cosine of the angle \( \theta \) between the ladder and the ground is given by:
\[
\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
Substituting the values:
\[
\cos(\theta) = \frac{5}{20} = 0.25
\]

### Step 2: Find \( \theta \) using the inverse cosine
\[
\theta = \cos^{-1}(0.25) \approx 75.5^\circ
\]

### Conclusion:
The angle formed is approximately \( 75.5^\circ \), which is within 3° of 75° and thus meets the safety protocol.

**Correct Response**: 
> Yes, the angle formed is approximately 76°.

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Would you like further details on this solution, or do you have any questions?

1. How does trigonometry help in calculating ladder angles?
2. What are safety considerations for ladder angles in different professions?
3. How would different wall distances affect the angle for a fixed ladder length?
4. What other trigonometric functions could be used to find similar angles?
5. How do companies determine safe angle ranges for ladder placement?

**Tip:** When using a ladder, always check the placement angle for stability and safety.

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?

Calculate whether a 20-foot ladder placed 5 feet from a wall meets safety protocol by finding the angle with trigonometry. Learn how Tammy can ensure safe ladder use using the cosine function and inverse cosine calculations. This problem covers key trigonometric concepts suitable for Grades 9-11.

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