12 ft I 4 ft A child 4 ft tall is standing d ft away from a street lamp that is 12 ft tall. The shadow cast by the light shining on the child has length I. Write an equation that represents the length, , as a function of d.
12 ft I 4 ft A child 4 ft tall is standing d ft away from a street lamp that is 12 ft tall. The shadow cast by the light shining on the child has length I. Write an equation that represents the length, , as a function of d.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter87: An Introduction To G- And M-codes For Cnc Programming
Section: Chapter Questions
Problem 22A
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Question
**Explanation of the Diagram:**
The diagram shows a situation involving a child standing near a street lamp. Here are the details provided:
1. **Street Lamp**: It is depicted to the right of the child and is 12 feet tall.
2. **Child**: The child, standing to the left of the street lamp, is 4 feet tall.
3. **Distance**: The child is standing \( d \) feet away from the base of the street lamp.
4. **Shadow**: The shadow cast by the light, shining from the street lamp onto the child, has a length denoted as \( l \).
Two right triangles are formed in the diagram:
- One smaller triangle representing the child's height and the length of the shadow.
- One larger triangle representing the height of the street lamp and the total length from the street lamp to the tip of the shadow (which includes both \( d \) and \( l \)).
---
**Problem Statement:**
A child 4 feet tall is standing \( d \) feet away from a street lamp that is 12 feet tall. The shadow cast by the light shining on the child has length \( l \).
Write an equation that represents the length, \( l \), as a function of \( d \).
**Hint:** Notice that the triangles are similar, so the ratios of their corresponding sides are equal.
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This problem uses the concept of similar triangles to relate the child's height and the shadow with the street lamp and its shadow, forming a basis for establishing the equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe91e659-0274-4af0-b893-ea272a52ff02%2F1d771788-c6b2-438f-86b8-ec51adbeddc5%2F67ez83c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Image Transcription for Educational Website:**
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### Questions 8-10 all involve the same setup:
**Explanation of the Diagram:**
The diagram shows a situation involving a child standing near a street lamp. Here are the details provided:
1. **Street Lamp**: It is depicted to the right of the child and is 12 feet tall.
2. **Child**: The child, standing to the left of the street lamp, is 4 feet tall.
3. **Distance**: The child is standing \( d \) feet away from the base of the street lamp.
4. **Shadow**: The shadow cast by the light, shining from the street lamp onto the child, has a length denoted as \( l \).
Two right triangles are formed in the diagram:
- One smaller triangle representing the child's height and the length of the shadow.
- One larger triangle representing the height of the street lamp and the total length from the street lamp to the tip of the shadow (which includes both \( d \) and \( l \)).
---
**Problem Statement:**
A child 4 feet tall is standing \( d \) feet away from a street lamp that is 12 feet tall. The shadow cast by the light shining on the child has length \( l \).
Write an equation that represents the length, \( l \), as a function of \( d \).
**Hint:** Notice that the triangles are similar, so the ratios of their corresponding sides are equal.
---
This problem uses the concept of similar triangles to relate the child's height and the shadow with the street lamp and its shadow, forming a basis for establishing the equation.
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