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.