Pregunta
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.
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The stone tower’s shadow will be 24 meters long.
Solución
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
Cross-multiplying to solve for
Answer: 24
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Simplifique esta solución 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:
Cross-multiplying gives us:
Calculating the right side:
Now, we can solve for
Therefore, the stone tower’s shadow will be 24 meters long.
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