To solve this problem, we can break it down using trigonometry. Here's a step-by-step approach:

Information Given:

• Height of the cliff: 215 feet
• Andrea's eye level is 5.25 feet above the ground
• Angle of elevation: 42°
• We need to find the horizontal distance from Andrea to the base of the cliff.

Step-by-Step Solution:

1. Calculate the height difference between the top of the cliff and Andrea's eye level: $\text{Height difference} = 215 \, \text{ft} - 5.25 \, \text{ft} = 209.75 \, \text{ft}$

2. Use the tangent function to find the horizontal distance: The tangent of an angle is given by the formula: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ Where:

   • $\theta = 42^\circ$ (the angle of elevation)
   • The opposite side is the height difference (209.75 feet)
   • The adjacent side is the horizontal distance (which we want to find)

   Rearranging the formula to solve for the adjacent side (horizontal distance): $\text{adjacent} = \frac{\text{opposite}}{\tan(\theta)}$ $\text{horizontal distance} = \frac{209.75}{\tan(42^\circ)}$

3. Calculate the horizontal distance: $\text{horizontal distance} \approx \frac{209.75}{0.9004} \approx 232.0 \, \text{ft}$

Final Answer:

Andrea is approximately 232.0 feet from the base of the cliff.

Would you like any further clarification on this calculation? Let me know if you need more details!

Here are some related questions you may find interesting:

1. How do you calculate the tangent of an angle?
2. How would the result change if the angle of elevation were different?
3. What would happen to the horizontal distance if Andrea’s eye level was lower or higher?
4. How can you use trigonometry to solve real-world problems like this one?
5. What is the difference between the tangent, sine, and cosine functions in trigonometry?

Tip: Always double-check the angle units! Trigonometric functions use radians in some contexts, but degrees are the most common in most real-world applications like this one.