A flag pole that is 15 feet tall casts a shadow that is 20 feet long. At the same time of day, the shadow of a nearby tree is 38.5 feet long.
 
How tall is the tree?

To solve this problem, we can use the concept of similar triangles. The flagpole and its shadow form one right triangle, and the tree and its shadow form another right triangle. Since the triangles are similar, the ratios of the corresponding sides are equal.

Given:
- Height of the flagpole = 15 feet
- Length of the flagpole's shadow = 20 feet
- Length of the tree's shadow = 38.5 feet

Let the height of the tree be \( h \) feet. We set up the proportion:

\[
\frac{\text{Height of Flagpole}}{\text{Length of Flagpole's Shadow}} = \frac{\text{Height of Tree}}{\text{Length of Tree's Shadow}}
\]

\[
\frac{15}{20} = \frac{h}{38.5}
\]

Now, solve for \( h \):

\[
h = \frac{15}{20} \times 38.5
\]

\[
h = 0.75 \times 38.5 = 28.875 \text{ feet}
\]

So, the height of the tree is **28.875 feet**.

Would you like further details or have any questions? Here are 5 related questions you might find interesting:

1. How would the height of the tree change if the flagpole's height was different?
2. Can you use this method to find the height of a building given its shadow and the shadow of a smaller object?
3. What would happen to the shadow length if the sun were higher in the sky?
4. How do you derive the height of an object if you know the angle of elevation of the sun?
5. Could you solve this problem if only the angles were known instead of the shadow lengths?

**Tip:** Remember, similar triangles are a powerful tool for solving real-world problems involving heights and distances!

Learn how to calculate the height of a tree using the concept of similar triangles. Given the heights and shadow lengths of a flag pole and a tree, this problem involves applying proportions to find the height of the tree. Suitable for students in Grades 7-9.

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