If an n-sided regular polygon is inscribed in a circle of radius r, as shown in the figure below, then n-isosceles triangles fill the circle. Based on the statement and figure above answer the following: Express h and the base b of the isosceles triangle shown in terms of θ and r. Express the area of the isosceles triangle in terms of θ and r. Use trig identities as needed. Describe what happens as n goes to infinity, (notice the polygon fills the circle, the angle θ goes to zero) Use special limit rules to discuss your response, you may use any graphing tool to support your response.
If an n-sided regular polygon is inscribed in a circle of radius r, as shown in the figure below, then n-isosceles triangles fill the circle. Based on the statement and figure above answer the following: Express h and the base b of the isosceles triangle shown in terms of θ and r. Express the area of the isosceles triangle in terms of θ and r. Use trig identities as needed. Describe what happens as n goes to infinity, (notice the polygon fills the circle, the angle θ goes to zero) Use special limit rules to discuss your response, you may use any graphing tool to support your response.
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 11CT
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If an n-sided regular
Based on the statement and figure above answer the following:
- Express h and the base b of the isosceles triangle shown in terms of θ and r.
- Express the area of the isosceles triangle in terms of θ and r. Use trig identities as needed.
- Describe what happens as n goes to infinity, (notice the polygon fills the circle, the angle θ goes to zero)
- Use special limit rules to discuss your response, you may use any graphing tool to support your response.
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