To solve this problem, we can use similar triangles. The triangles formed by the tree and its shadow and by the person and their maximum shadow distance are proportional.

The height of the tree is 35 feet, and its shadow length is 150 feet. The person is 7 feet tall, and we want to find the distance $x$ from the person to the base of the tree to ensure they stay within the shadow.

Using the ratio of the heights and shadows:

$\frac{35}{150} = \frac{7}{x}$

Cross-multiplying to solve for $x$:

$35x = 7 \times 150$

$35x = 1050$

$x = \frac{1050}{35} = 30$

Thus, the distance between you and the tree is 30 feet.

Would you like more details or have any questions?

Here are some related questions to explore further:

1. What if the tree were taller, say 50 feet? How would that affect the shadow distance?
2. How would the calculation change if the sun’s angle changed, affecting the shadow length?
3. If the person were shorter, like 5 feet, what would their maximum distance be?
4. How would you solve this if the shadow length of the tree wasn't given?
5. Can this method be used to determine the shadow length of any object given its height and shadow proportions?

Tip: Similar triangles are a powerful tool to find distances and heights indirectly, especially in problems involving shadows and angles.