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  64°
 , how far from the base of the tree am I?

 

Round your answer to four decimal places.

 

I am about  

 feet away from the base of the tree.

To solve this problem, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side:

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

In this case:

- 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 is what we are solving for.
- The angle \( \theta \) is given as \( 64^\circ \).

Using the formula:

\[
\tan(64^\circ) = \frac{370}{\text{distance}}
\]

Now, solve for the distance:

\[
\text{distance} = \frac{370}{\tan(64^\circ)}
\]

Let me calculate that for you.You are approximately **180.4611 feet** away from the base of the tree.

Do you want further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the distance change if the angle of elevation were 45° instead of 64°?
2. What trigonometric function would you use if the distance and angle were known, but you needed to find the height of the tree?
3. How does the angle of elevation affect the distance from the tree?
4. Can you calculate the height of a tree if the angle of elevation is 30° and you stand 50 feet away from the base?
5. How would you solve this problem if the tree grew on a hill inclined at 10°?

**Tip:** When using trigonometric functions, ensure your calculator is set to the correct mode (degrees or radians) depending on the angle units.

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 64°, how far from the base of the tree am I? Round your answer to four decimal places.

Learn how to calculate the distance from the base of a 370-foot tall giant redwood using a 64° angle of elevation with trigonometry. This detailed solution involves applying the tangent function to solve for the distance. Perfect for students in Grades 9-12.

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