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The figure shows part of a regular n-gon inscribed in a circle of radius r. Use the figure to answer the questions and derive a formula for the circumference of a circle with radius r.

 

1. The regular n-gon can be divided into n congruent isosceles triangles, each with a vertex angle of measure. What is the measure of 360 degrees/n in terms of n? Explain.

2. Use the sine ratio to write an expression for x in terms of r and n. Show your work.

3. Use the expression you found for x to write an expression for the perimeter of the inscribed n-gon.

4. Your expression for the perimeter of the inscribed n-gon should contain the factor n sin (180 degrees/n). Use technology to help you explain what happens to the value of n sin (180 degrees/n) as n gets larger and larger. (Hint: Describe how this information relates to the circumference of a circle.)

5. As n gets larger and larger, the perimeter of the inscribed n-gon gets closer and closer to the circle. What does the expression in question 2 and your answer to question 4 tell you about the formula for the circumference of a circle? Explain.

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Acceptfully  May 30, 2017
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2+0 Answers

 #1
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hey the answer to this quetion  is 98

Guest May 30, 2017
 #2
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Is this the same question that you have?

https://web2.0calc.com/questions/i-can-t-do-math

smiley

hectictar  May 30, 2017
edited by hectictar  May 30, 2017
edited by hectictar  May 30, 2017

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