An elm tree casts a shadow that is 15 feet long. A wooden column near the elm tree casts a shadow that is 30 feet long. If the elm tree is 8 feet tall, how tall is the wooden column? Write your answer as a whole number or a decimal. Do not round.

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UpStudy AI · Accepted Answer

To determine the height of the wooden column, we can use the concept of similar triangles. The ratio of the height of an object to the length of its shadow remains constant when the sun's angle is the same.

Given:
- Elm tree height = 8 feet
- Elm tree shadow = 15 feet
- Wooden column shadow = 30 feet

Let's denote the height of the wooden column as $$ h $$.

Set up the proportion based on the similar triangles:

$$
\frac{\text{Elm tree height}}{\text{Elm tree shadow}} = \frac{\text{Wooden column height}}{\text{Wooden column shadow}}
$$

$$
\frac{8}{15} = \frac{h}{30}
$$

Now, solve for $$ h $$:

$$
h = \frac{8 \times 30}{15} = \frac{240}{15} = 16
$$

**Answer:**  
16
The wooden column is 16 feet tall.

An elm tree casts a shadow that is 15 feet long. A wooden column near the elm tree casts a shadow that is 30 feet long. If the elm tree is 8 feet tall, how tall is the wooden column? Write your answer as a whole number or a decimal. Do not round.

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