To solve this problem, we'll use the fact that the student and the tree, along with their respective shadows, form similar triangles. The key here is to set up a proportion using the corresponding parts of the triangles: the height of the student to the length of her shadow, and the height of the tree to the length of the tree's shadow.

1. Student’s height: The student is 5 feet 6 inches, which is 5.5 feet.
2. Student’s shadow: The shadow is 6 feet long.
3. Tree’s shadow: The shadow is 20 feet long.
4. We are asked to find the height of the tree (let’s call it h).

Using the property of similar triangles, we can set up the proportion:

$\frac{\text{Student's height}}{\text{Student's shadow}} = \frac{\text{Tree's height}}{\text{Tree's shadow}}$

Substitute the known values:

$\frac{5.5}{6} = \frac{h}{20}$

Now, solve for h:

$h = \frac{5.5 \times 20}{6} = \frac{110}{6} = 18.33 \, \text{ft}$

Thus, the height of the tree is 18.33 feet.

Let me know if you have any questions or need further details!

Related Questions:

1. How does the concept of similar triangles apply to other real-world situations?
2. What would happen if the student's shadow was longer than 6 feet?
3. How can we apply this method to find the height of other objects, like buildings or poles?
4. What other methods could be used to find the height of a tree?
5. If the tree's shadow was shorter, would the tree still be taller than the student?

Tip:

To solve similar triangle problems, always make sure to set up the correct proportion, ensuring that corresponding sides are compared (height to height, shadow to shadow).