https://file.aiquickdraw.com/mathbot/file/17260299296624rcnny1h.jpg

This problem can be solved using the concept of **similar triangles**, as both the tree and the statue cast shadows under the same sunlight conditions.

We are given:
- The tree's shadow length: 16 m
- The statue's height: 62 cm
- The statue's shadow length: 93 cm

We need to find the height of the tree.

### Step-by-step solution:

First, convert the shadow of the tree to centimeters so that all units are consistent:
\[
16 \, \text{m} = 1600 \, \text{cm}
\]

Now set up the ratio using the fact that the triangles are similar:
\[
\frac{\text{Height of Tree}}{\text{Shadow of Tree}} = \frac{\text{Height of Statue}}{\text{Shadow of Statue}}
\]

Substitute the known values:
\[
\frac{h}{1600} = \frac{62}{93}
\]

Now, solve for \( h \) (the height of the tree):
\[
h = \frac{62}{93} \times 1600
\]

Let me calculate this.The height of the tree is approximately **1066.67 cm**, or about **10.67 meters**.

Would you like further details on how this was calculated or have any questions?

Here are 5 related questions you could explore:
1. How do similar triangles help in solving real-world problems like this one?
2. Can this method be used to measure the height of tall objects in other contexts?
3. What assumptions are made when using shadows to calculate heights?
4. How would the solution change if the tree’s shadow length were measured at a different time of day?
5. How can the concept of scaling be applied to solve other geometry problems?

**Tip**: Always make sure the units in your equations are consistent (like converting meters to centimeters, if necessary).

A tree casts a shadow 16 m long. At the same time, the shadow cast by a 62-centimeter-tall statue is 93 cm long. Find the height of the tree.

Learn how to calculate the height of a tree based on its shadow using similar triangles. The problem involves comparing the shadow of a 62 cm tall statue and its 93 cm shadow to the tree's shadow of 16 m. Suitable for Grades 7-9.

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