Assuming that a  370
 -foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be  39°
 , how far from the base of the tree am I?

 

Round your answer to four decimal places.

 

I am about  
Number
 feet away from the base of the tree.

To solve this problem, we can use trigonometry. Specifically, we can apply the tangent function, since it relates the opposite side (height of the tree) and the adjacent side (distance from the tree) to the angle of elevation.

The formula we will use is:

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

Where:
- \( \theta = 39^\circ \) is the angle of elevation.
- The opposite side is the height of the tree, which is 370 feet.
- The adjacent side is the distance from the base of the tree, which we need to find.

Rearranging the formula to solve for the adjacent side (distance from the tree):

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

Substitute the known values:

\[
\text{adjacent} = \frac{370}{\tan(39^\circ)}
\]

Now, calculating this:

\[
\text{adjacent} = \frac{370}{0.8098} \approx 457.35 \text{ feet}
\]

Thus, you are approximately **457.3511 feet** away from the base of the tree.

Would you like more details on how to solve it step-by-step? Or do you have other questions related to this?

### Related Questions:
1. How do I calculate the angle of elevation if I know the distance from the tree and the height?
2. What is the difference between tangent and other trigonometric functions like sine and cosine?
3. Can this method be used for other real-world problems like measuring buildings or mountains?
4. How does the angle of elevation change if I move further away or closer to the tree?
5. What is the role of a calculator in solving trigonometric problems like this?

**Tip:** Always double-check your angle units. Make sure your calculator is set to the correct mode (degrees in this case).

Assuming that a 370-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 39°, how far from the base of the tree am I?

Learn how to calculate the distance from the base of a giant redwood tree using trigonometry. This step-by-step solution uses the tangent function to determine that if the height of the tree is 370 feet and the angle of elevation is 39°, the distance from the base is approximately 457.3511 feet. Suitable for high school students learning trigonometry.

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