To solve this problem, we can use the trigonometric relationship involving the tangent function in a right triangle. The relationship is:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Given:

• Height of the tree ($\text{opposite}$): $370 \, \text{ft}$
• Angle of elevation ($\theta$): $49^\circ$
• Distance from the base of the tree ($\text{adjacent}$): $x$ (to be found)

From the tangent formula:

$\tan(49^\circ) = \frac{370}{x}$

Rearrange to solve for $x$:

$x = \frac{370}{\tan(49^\circ)}$

Calculation:

1. Find $\tan(49^\circ)$ using a calculator: $\tan(49^\circ) \approx 1.1504$

2. Substitute into the equation: $x = \frac{370}{1.1504} \approx 321.4982 \, \text{ft}$

Final Answer:

The distance from the base of the tree is approximately:

$\boxed{321.4982 \, \text{ft}}$

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Would you like a detailed explanation of any step or a visualization of this problem? Here are five related questions to explore further:

1. How do you calculate the angle of elevation if the distance and height are given?
2. What is the sine and cosine of the angle in this scenario?
3. How would the distance change if the tree's height were doubled but the angle remained the same?
4. What if the ground is not level—how would this affect the calculations?
5. How do these trigonometric principles apply in real-world scenarios like surveying?

Tip: Always double-check angle measurements to ensure you're using the correct unit (degrees vs radians) in calculations!