We can solve this problem using trigonometry. Specifically, the tangent function, which relates the opposite side (the height of the tree) and the adjacent side (the horizontal distance from the tree).

Given:

• Height of the tree ($h$): $331 \, \text{feet}$
• Distance from the base ($d$): $100 \, \text{feet}$

We want to find the angle of elevation ($\theta$).

The tangent of the angle of elevation is given by: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d}$

Substitute the values: $\tan \theta = \frac{331}{100} = 3.31$

Now, to find $\theta$, take the arctangent ($\tan^{-1}$) of 3.31: $\theta = \tan^{-1}(3.31)$

Using a calculator: $\theta \approx 73.31^\circ$

Final Answer:

The angle of elevation to the top of the tree is approximately 73.31°.

---

Would you like a detailed explanation of the steps? Here are some related questions to expand your understanding:

1. What is the formula for finding angles of elevation or depression in trigonometry?
2. How does the distance from the tree's base affect the angle of elevation?
3. What would the angle of elevation be if the observer were twice as far from the tree?
4. How is the tangent function used in real-life scenarios like this?
5. Can you calculate the height of a tree if the angle of elevation and distance are known?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems!