To solve this problem, we can use similar triangles, as the angles between the sun’s rays, the tree, and its shadow are the same as the angles between the sun’s rays, you, and your shadow.

Here's a step-by-step approach:

1. Set Up the Triangles:

   • The tree and its shadow form a right triangle where:
     • The height of the tree is $30$ feet.
     • The shadow of the tree is $50$ feet.
   • You, being $6$ feet tall, would have a proportional shadow length that depends on your distance from the tree.

2. Calculate the Shadow Proportion: Using the similarity of triangles, we set up the following proportion based on the heights and shadow lengths:

   $\frac{\text{Height of tree}}{\text{Shadow of tree}} = \frac{\text{Your height}}{\text{Your shadow length}}$

   Substituting values:

   $\frac{30}{50} = \frac{6}{\text{Your shadow length}}$

3. Solve for Your Shadow Length: Cross-multiply to find your shadow length:

   $30 \times \text{Your shadow length} = 6 \times 50$

   $30 \times \text{Your shadow length} = 300$

   $\text{Your shadow length} = \frac{300}{30} = 10 \text{ feet}$

4. Determine Your Position Relative to the Tree: Since the tree’s shadow is $50$ feet long, and your shadow length is $10$ feet, you need to be within the length of the tree's shadow to be fully covered by it. Thus, you can stand anywhere up to $50 - 10 = 40$ feet away from the tree and remain completely in its shadow.

Final Answer:

You can stand up to 40 feet away from the tree and still be completely in the shadow of the tree.

Would you like further details or have any questions?

---

Here are some questions to deepen understanding:

1. How would the solution change if the height of the tree was doubled?
2. What happens to the distance you can stand away from the tree if your height increases?
3. How would the calculation change if the sun were at a lower angle?
4. If the shadow of the tree were shorter, how would it affect your maximum distance?
5. How would this apply if you had multiple trees in a row?

Tip: Always draw a diagram for problems involving similar triangles and proportional relationships to visualize the relationships between elements.