Que A water sprinkler sprays water over a distance of 20 feet while rotating through an angle of 140°. What area of lawn receives water? 140 20 ft The area A of the sector is square feet. (Type an integer or decimal rounded to two decimal places as needed.)
Que A water sprinkler sprays water over a distance of 20 feet while rotating through an angle of 140°. What area of lawn receives water? 140 20 ft The area A of the sector is square feet. (Type an integer or decimal rounded to two decimal places as needed.)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Sprinkler Coverage Area Calculation
A water sprinkler sprays water over a distance of 20 feet while rotating through an angle of 140°. What area of lawn receives water?
Here is a diagram illustrating the sprinkler's coverage area:
(The diagram shows a sector with a central angle of 140° and a radius of 20 feet.)
#### Question
The area \(A\) of the sector is \(\_\_\_\_\_\_\) square feet.
(Type an integer or decimal rounded to two decimal places as needed.)
---
### Calculation and Explanation
To find the area of the sector formed by the sprinkler, we use the formula for the area of a sector:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
Where:
- \(\theta\) is the central angle (in degrees)
- \(r\) is the radius of the sector (distance the water is sprayed)
Given:
- \(\theta = 140°\)
- \(r = 20\) feet
Substituting the values:
\[ A = \frac{140}{360} \times \pi \times 20^2 \]
Now, calculate the area:
\[ A = \frac{140}{360} \times \pi \times 400 \]
\[ A = \frac{7}{18} \times \pi \times 400 \]
\[ A = \frac{7 \times 400}{18} \times \pi \]
\[ A = \frac{2800}{18} \times \pi \]
\[ A \approx 155.56 \pi \]
\[ A \approx 488.69 \text{ square feet} \]
Therefore, the area of the sector is approximately 488.69 square feet.
---
Please enter your answer in the answer box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2bbef39-13a9-4a3a-ae0f-bc83a28a95a1%2F92cae7c8-2688-4cd0-94b6-0375ddd313d5%2Fgnr45ad_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sprinkler Coverage Area Calculation
A water sprinkler sprays water over a distance of 20 feet while rotating through an angle of 140°. What area of lawn receives water?
Here is a diagram illustrating the sprinkler's coverage area:
(The diagram shows a sector with a central angle of 140° and a radius of 20 feet.)
#### Question
The area \(A\) of the sector is \(\_\_\_\_\_\_\) square feet.
(Type an integer or decimal rounded to two decimal places as needed.)
---
### Calculation and Explanation
To find the area of the sector formed by the sprinkler, we use the formula for the area of a sector:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
Where:
- \(\theta\) is the central angle (in degrees)
- \(r\) is the radius of the sector (distance the water is sprayed)
Given:
- \(\theta = 140°\)
- \(r = 20\) feet
Substituting the values:
\[ A = \frac{140}{360} \times \pi \times 20^2 \]
Now, calculate the area:
\[ A = \frac{140}{360} \times \pi \times 400 \]
\[ A = \frac{7}{18} \times \pi \times 400 \]
\[ A = \frac{7 \times 400}{18} \times \pi \]
\[ A = \frac{2800}{18} \times \pi \]
\[ A \approx 155.56 \pi \]
\[ A \approx 488.69 \text{ square feet} \]
Therefore, the area of the sector is approximately 488.69 square feet.
---
Please enter your answer in the answer box.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning