(a)
Find the perimeter of a regular
(a)
Answer to Problem 24WE
Explanation of Solution
Formula Used:
Law of Sines:
Calculation:
The n -gon has n sides and if we join the sides to the centre of the circle, it forms n isosceles
Since there are n equal triangles, the angle to the centre of each triangle is
Let base of each triangle is x .
In the isosceles triangle , the central angle is
Use the law of sines to find x :
Since the n -gon has n sides , and one of the side is x , so , the perimeter of the n -gon inscribed inside a unit circle is nx :
The n -gon circumscribed about the unit circle has n sides and if we join the sides to the centre of the circle, it forms n triangles:
Since there are n equal triangles, the angle to the centre of each triangle is
So, the central angle of the right angled triangle that bisects the triangle is
Let base of each right angled triangle is x and height is 1.
So,
Eace side of the n - gon is 2x =
Since the n -gon has n sides , and one of the side is
(b)
Find where the number is approached when n gets larger and larger:
(b)
Answer to Problem 24WE
both the numbers approaches 0 as n becomes larger and larger.
Explanation of Solution
Calculation :
As n becomes larger and larger ,
Hence , both the numbers approaches 0 as n becomes larger and larger.
Chapter 12 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
Additional Math Textbook Solutions
Intermediate Algebra for College Students (7th Edition)
College Algebra (6th Edition)
Algebra and Trigonometry (6th Edition)
Linear Algebra and Its Applications (5th Edition)
Elementary Algebra
College Algebra (5th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education