Question
Question A tree casts a 38 foot shadow at the same time a boy casts a 9 foot shadow. If the boy is 5.5 feet tall, how tall is the tree? Interpret the answer. Aelect the correct answer below: A 38 foot tall tree casts a 23.2 foot shadow. A 23.2 foot tall boy casts a tree casts a 23.2 foot shadow. A 23.2 foot tall tree casts a 38 foot shadow.
Ask by Nunez Dunn. in the United States
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A 38-foot tall tree casts a 23.2-foot shadow.
Solution
Given that the tree casts a 38 foot shadow at the same time a boy casts a 9 foot shadow, and the boy is 5.5 feet tall, we can use the concept of similar triangles to find the height of the tree.
Let's denote the height of the tree as \( h \) and the height of the boy as 5.5 feet. The ratio of the height of the tree to the height of the boy is equal to the ratio of the length of the tree's shadow to the length of the boy's shadow.
Therefore, we have:
\[ \frac{h}{5.5} = \frac{38}{9} \]
To find the height of the tree, we can solve this equation for \( h \).
\[ h = \frac{5.5 \times 38}{9} \]
Let's calculate the height of the tree.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{5.5\times 38}{9}\)
- step1: Multiply the numbers:
\(\frac{209}{9}\)
The height of the tree is approximately 23.2 feet.
Therefore, the correct answer is:
A 38 foot tall tree casts a 23.2 foot shadow.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
This problem can be solved using the concept of similar triangles, where the height of the objects is proportional to the length of their shadows. Given that the boy is 5.5 feet tall and has a 9-foot shadow, we can set up a proportion: 5.5 feet / 9 feet = height of the tree / 38 feet. Solving this gives us approximately 23.2 feet as the height of the tree. In essence, the tree is approximately 23.2 feet tall, and it casts a longer shadow due to being taller, a wonderful example of how similar triangles work in real life, especially in architecture and nature. So next time you see a tall tree, just remember it's all about proportions and angles in the great outdoors!
