Question
A lookout tower that is 15 meters tall casts a shadow 8 meters long. If a nearby stone tower is 45 meters tall, how long will the stone tower's shadow be? Write your answer as a whole number or a decimal. Do not round.
Ask by Best Cook. in the United States
Jan 23,2025
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Tutor-Verified Answer
Answer
The stone tower's shadow will be 24 meters long.
Solution
To determine the length of the stone tower's shadow, we can use the concept of similar triangles. The ratio of the height of a tower to the length of its shadow remains constant when the sun's angle is the same.
Given:
- Lookout tower height = 15 meters
- Lookout tower's shadow = 8 meters
- Stone tower height = 45 meters
Let \( x \) be the length of the stone tower's shadow. Setting up the proportion:
\[
\frac{15}{8} = \frac{45}{x}
\]
Cross-multiplying to solve for \( x \):
\[
15x = 45 \times 8
\]
\[
15x = 360
\]
\[
x = \frac{360}{15}
\]
\[
x = 24
\]
**Answer:** 24
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Simplify this solution Extra Insights
To find the length of the stone tower's shadow, we can use the concept of similar triangles. The ratio of the height of the lookout tower to its shadow's length is the same as that of the stone tower to its shadow's length. Let's set up the proportion: \(\frac{15 \text{ m}}{8 \text{ m}} = \frac{45 \text{ m}}{x}\) Cross-multiplying gives us: \(15x = 8 \cdot 45\) Calculating the right side: \(8 \cdot 45 = 360\) Now, we can solve for \(x\): \(15x = 360\) \(x = \frac{360}{15} = 24\) Therefore, the stone tower's shadow will be **24 meters long**.
