Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Calculating the Apothem of a Regular Pentagon
**Problem:**
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place.
**Diagram:**
- The image shows a regular pentagon with one of its side lengths labeled as \(7.6 \, \text{m}\).
- The apothem of the pentagon is represented with a line segment labeled 'a' which extends from the center of the pentagon to the midpoint of one of its sides.
### Explanation:
A regular pentagon is a five-sided polygon with all sides and angles equal. The apothem of a regular polygon can be calculated using the following formula:
\[ \text{Apothem} = \frac{s}{2 \tan(\pi/n)} \]
Where:
- \(s = 7.6 \, \text{m}\) (the length of a side)
- \(n = 5\) (the number of sides in a pentagon)
- \(\pi \approx 3.14159\)
### Calculation:
1. Calculate the angle for tan:
\[ \text{Angle} = \frac{\pi}{5} \]
2. Find the value of \(\tan(\pi / 5)\).
3. Using the apothem formula, substitute in the values:
\[ \text{Apothem} = \frac{7.6}{2 \tan(\pi / 5)} \]
4. Perform the calculations to find the apothem value and round to one decimal place.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc65d712c-e651-45fa-aada-1fa4337702ab%2Fdef20fb3-6a9b-43bc-a71a-6fada5ab593f%2F3lrsbmr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Apothem of a Regular Pentagon
**Problem:**
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place.
**Diagram:**
- The image shows a regular pentagon with one of its side lengths labeled as \(7.6 \, \text{m}\).
- The apothem of the pentagon is represented with a line segment labeled 'a' which extends from the center of the pentagon to the midpoint of one of its sides.
### Explanation:
A regular pentagon is a five-sided polygon with all sides and angles equal. The apothem of a regular polygon can be calculated using the following formula:
\[ \text{Apothem} = \frac{s}{2 \tan(\pi/n)} \]
Where:
- \(s = 7.6 \, \text{m}\) (the length of a side)
- \(n = 5\) (the number of sides in a pentagon)
- \(\pi \approx 3.14159\)
### Calculation:
1. Calculate the angle for tan:
\[ \text{Angle} = \frac{\pi}{5} \]
2. Find the value of \(\tan(\pi / 5)\).
3. Using the apothem formula, substitute in the values:
\[ \text{Apothem} = \frac{7.6}{2 \tan(\pi / 5)} \]
4. Perform the calculations to find the apothem value and round to one decimal place.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning