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.