A fence 6 feet tall runs parallel to a tall building at a distance of 2 ft from the building as shown in the diagram. We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. L(0) : LADDER [A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) Type theta for 9. = 6 ft feet [B] Now, find the derivative, L'(0). Type theta for 0. L'(0) = [C] Once you find the value of that makes L'(0) = 0, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.) L(0 min)
A fence 6 feet tall runs parallel to a tall building at a distance of 2 ft from the building as shown in the diagram. We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. L(0) : LADDER [A] First, find a formula for the length of the ladder in terms of 0. (Hint: split the ladder into 2 parts.) Type theta for 9. = 6 ft feet [B] Now, find the derivative, L'(0). Type theta for 0. L'(0) = [C] Once you find the value of that makes L'(0) = 0, substitute that into your original function to find the length of the shortest ladder. (Give your answer accurate to 5 decimal places.) L(0 min)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 72RE
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![### Title: Finding the Shortest Ladder Length
#### Introduction
A fence 6 feet tall runs parallel to a tall building at a distance of 2 feet from the building as shown in the diagram.
#### Diagram Description
- **Diagram Details**:
- A right triangle is formed with the ground, the ladder, and the top of the fence as vertices.
- The ladder leans against the building, touching it at one end and the ground at the other, intersecting the top of the fence.
- There is an angle θ between the ground and the ladder.
- The vertical side of the triangle from the ground to the top of the fence is 6 feet.
- The horizontal distance from the fence to the building is 2 feet.
![Figure Description]
- The ladder is split into two parts:
- From the ground to the top of the fence.
- From the fence to the wall of the building.
#### Problem Description
We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building.
#### [A] Finding the Ladder Length Formula
1. **Instruction**: Find a formula for the length of the ladder in terms of θ.
- **Hint**: Split the ladder into 2 parts.
2. **Action**:
- Type theta for θ.
- Fill in the formula for \( L(\theta) \).
\[ L(\theta) = \]
<input type="text" placeholder="Enter formula here">
#### [B] Finding the Derivative
1. **Instruction**: Find the derivative, \( L'(\theta) \).
2. **Action**:
- Type theta for θ.
- Fill in the derivative.
\[ L'(\theta) = \]
<input type="text" placeholder="Enter derivative here">
#### [C] Minimizing the Ladder Length
1. **Instruction**: Once you find the value of θ that makes \( L'(\theta) = 0 \), substitute that into your original function to find the length of the shortest ladder.
- **Note**: Give your answer accurate to 5 decimal places.
2. **Action**:
- Fill in the minimum length of the ladder.
\[ L(\theta_{\text{min}}) \approx \]
<input type="text" placeholder="Enter length here"> feet
---
Ensure to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F621ac9f8-2dbb-4715-ab7b-42c3ebc90b44%2Ff0f9ea6c-26bb-49b6-9bea-7f66c82ffefd%2Fbn8mwma_processed.png&w=3840&q=75)
Transcribed Image Text:### Title: Finding the Shortest Ladder Length
#### Introduction
A fence 6 feet tall runs parallel to a tall building at a distance of 2 feet from the building as shown in the diagram.
#### Diagram Description
- **Diagram Details**:
- A right triangle is formed with the ground, the ladder, and the top of the fence as vertices.
- The ladder leans against the building, touching it at one end and the ground at the other, intersecting the top of the fence.
- There is an angle θ between the ground and the ladder.
- The vertical side of the triangle from the ground to the top of the fence is 6 feet.
- The horizontal distance from the fence to the building is 2 feet.
![Figure Description]
- The ladder is split into two parts:
- From the ground to the top of the fence.
- From the fence to the wall of the building.
#### Problem Description
We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building.
#### [A] Finding the Ladder Length Formula
1. **Instruction**: Find a formula for the length of the ladder in terms of θ.
- **Hint**: Split the ladder into 2 parts.
2. **Action**:
- Type theta for θ.
- Fill in the formula for \( L(\theta) \).
\[ L(\theta) = \]
<input type="text" placeholder="Enter formula here">
#### [B] Finding the Derivative
1. **Instruction**: Find the derivative, \( L'(\theta) \).
2. **Action**:
- Type theta for θ.
- Fill in the derivative.
\[ L'(\theta) = \]
<input type="text" placeholder="Enter derivative here">
#### [C] Minimizing the Ladder Length
1. **Instruction**: Once you find the value of θ that makes \( L'(\theta) = 0 \), substitute that into your original function to find the length of the shortest ladder.
- **Note**: Give your answer accurate to 5 decimal places.
2. **Action**:
- Fill in the minimum length of the ladder.
\[ L(\theta_{\text{min}}) \approx \]
<input type="text" placeholder="Enter length here"> feet
---
Ensure to
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