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This is a trigonometric problem involving two similar triangles. We have to calculate the height of the tree (\( h \)) using the properties of similar triangles and ratios.

Here’s a step-by-step breakdown of the problem:

- The two triangles \( \triangle ABE \) and \( \triangle ACD \) are similar because they share the same angle at \( A \) and both are right-angled triangles.
- The height \( BE \) is 2 meters, and the horizontal distance \( AB \) is 5 meters.
- The total horizontal distance from \( A \) to \( C \) is 35 meters (5 meters from \( A \) to \( B \), plus 30 meters from \( B \) to \( C \)).

Using the property of similar triangles:
\[
\frac{BE}{AB} = \frac{CD}{AC}
\]
Substitute the known values:
\[
\frac{2}{5} = \frac{h}{35}
\]

Now, let's solve for \( h \):
\[
h = \frac{2}{5} \times 35
\]
\[
h = \frac{70}{5} = 14 \text{ meters}
\]

Thus, the height \( h \) of the tree is \( 14 \) meters.

Would you like further details, or do you have any questions? Here are some related questions:

1. How do similar triangles help in solving height-related problems?
2. How would you solve the problem if the distance from \( A \) to \( C \) were different?
3. What are the key trigonometric ratios used in similar triangles?
4. Can you calculate the angle \( \theta \) at \( A \) using trigonometric functions?
5. How can we verify if two triangles are similar in any geometry problem?

**Tip:** In problems involving similar triangles, setting up proportional relationships between corresponding sides is the key to solving for unknown lengths.

Calculate h, the height of the tree. Give your answer as an integer or as a fraction in its simplest form.

Learn how to calculate the height of a tree using the properties of similar triangles in this step-by-step problem. This problem uses geometric ratios and key theorems to solve for an unknown height. Suitable for students in Grades 9-10.

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