The problem you shared is about using proportionality between the heights of two trees and the lengths of their shadows.

Given:

• First tree height: 15 meters
• First tree shadow length: 10 meters
• Second tree shadow length: 14.4 meters
• We need to calculate the height of the second tree (denoted as $h_2$).

Since height and shadow length are directly proportional:

$\frac{\text{Height of first tree}}{\text{Shadow of first tree}} = \frac{\text{Height of second tree}}{\text{Shadow of second tree}}$

Substituting the known values: $\frac{15}{10} = \frac{h_2}{14.4}$

Now, solve for $h_2$: $h_2 = \frac{15 \times 14.4}{10} = 21.6 \, \text{meters}$

Answer:

The height of the second tree is $21.6$ meters (to 1 decimal place).

Let me know if you would like more details or have further questions.

Here are 5 related questions to expand your understanding:

1. What is the formula for direct proportionality?
2. How would the solution change if the shadow length of the second tree were halved?
3. What are other real-world examples of direct proportionality?
4. How would you calculate the shadow length if the height of the second tree were known instead?
5. Can you find the shadow length of a tree that is 25 meters tall using this proportionality?

Tip: Always check if units are consistent across the problem when applying proportional relationships.