To determine the length of the shadow cast by a tree that is 18 meters tall, we can use the concept of similar triangles. When two objects cast shadows under the same lighting conditions, the ratios of their heights to their shadow lengths are equal.
1. Identify the given information:
- Height of the flagpole: 15 meters
- Shadow length of the flagpole: 35 meters
- Height of the tree: 18 meters
- Shadow length of the tree: Unknown (let's call it [tex]\( x \)[/tex] meters)
2. Set up the proportion:
[tex]\[
\frac{\text{Height of the flagpole}}{\text{Shadow length of the flagpole}} = \frac{\text{Height of the tree}}{\text{Shadow length of the tree}}
\][/tex]
Substitute the given values:
[tex]\[
\frac{15}{35} = \frac{18}{x}
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to cross-multiply and then isolate [tex]\( x \)[/tex]:
[tex]\[
15 \cdot x = 18 \cdot 35
\][/tex]
[tex]\[
15x = 630
\][/tex]
[tex]\[
x = \frac{630}{15}
\][/tex]
4. Calculate the value of [tex]\( x \)[/tex]:
[tex]\[
x = 42
\][/tex]
5. Conclude the solution:
The shadow cast by a tree that is 18 meters tall is 42 meters.
Therefore, the shadow cast by a 18-meter high tree is 42 meters.
