Inradius of Hendecagon given Circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inradius of Hendecagon = (sin(pi/11)*Circumradius of Hendecagon)/tan(pi/11)
ri = (sin(pi/11)*rc)/tan(pi/11)
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
Variables Used
Inradius of Hendecagon - (Measured in Meter) - The Inradius of Hendecagon is defined as the radius of the circle which is inscribed inside the Hendecagon.
Circumradius of Hendecagon - (Measured in Meter) - The Circumradius of Hendecagon is the radius of a circumcircle touching each of the vertices of Hendecagon.
STEP 1: Convert Input(s) to Base Unit
Circumradius of Hendecagon: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = (sin(pi/11)*rc)/tan(pi/11) --> (sin(pi/11)*9)/tan(pi/11)
Evaluating ... ...
ri = 8.63543676253047
STEP 3: Convert Result to Output's Unit
8.63543676253047 Meter --> No Conversion Required
FINAL ANSWER
8.63543676253047 8.635437 Meter <-- Inradius of Hendecagon
(Calculation completed in 00.004 seconds)

Credits

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Walchand College of Engineering (WCE), Sangli
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10+ Inradius of Hendecagon Calculators

Inradius of Hendecagon given Diagonal across Three Sides
Go Inradius of Hendecagon = (((Diagonal across Three Sides of Hendecagon*sin(pi/11))/sin((3*pi)/11)))/(2*tan(pi/11))
Inradius of Hendecagon given Diagonal across Five Sides
Go Inradius of Hendecagon = (((Diagonal across Five Sides of Hendecagon*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11))
Inradius of Hendecagon given Diagonal across Four Sides
Go Inradius of Hendecagon = (((Diagonal across Four Sides of Hendecagon*sin(pi/11))/sin((4*pi)/11)))/(2*tan(pi/11))
Inradius of Hendecagon given Diagonal across Two Sides
Go Inradius of Hendecagon = (((Diagonal across Two Sides of Hendecagon*sin(pi/11))/sin((2*pi)/11)))/(2*tan(pi/11))
Inradius of Hendecagon given Width
Go Inradius of Hendecagon = (((Width of hendecagon*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11))
Inradius of Hendecagon given Area
Go Inradius of Hendecagon = sqrt(Area of Hendecagon*(4*tan(pi/11))/11)/(2*tan(pi/11))
Inradius of Hendecagon given Circumradius
Go Inradius of Hendecagon = (sin(pi/11)*Circumradius of Hendecagon)/tan(pi/11)
Inradius of Hendecagon given Height
Go Inradius of Hendecagon = (Height of Hendecagon*tan(pi/22))/(tan(pi/11))
Inradius of Hendecagon given Perimeter
Go Inradius of Hendecagon = (Perimeter of Hendecagon)/(22*tan(pi/11))
Inradius of Hendecagon
Go Inradius of Hendecagon = Side of Hendecagon/(2*tan(pi/11))

Inradius of Hendecagon given Circumradius Formula

Inradius of Hendecagon = (sin(pi/11)*Circumradius of Hendecagon)/tan(pi/11)
ri = (sin(pi/11)*rc)/tan(pi/11)

What is Hendecagon?

A Hendecagon is an 11-sided polygon, also variously known as an undecagon or unidecagon. The term "hendecagon" is preferable to the other two since it uses the Greek prefix and suffix instead of mixing a Roman prefix and Greek suffix. A Hendecagon with vertices equally spaced around a circle and with all sides the same length is a regular polygon known as a regular Hendecagon.

How to Calculate Inradius of Hendecagon given Circumradius?

Inradius of Hendecagon given Circumradius calculator uses Inradius of Hendecagon = (sin(pi/11)*Circumradius of Hendecagon)/tan(pi/11) to calculate the Inradius of Hendecagon, The inradius of Hendecagon given Circumradius formula is defined as the straight line connecting the incenter of the Hendecagon and any point on the circle that touches all edges of the Hendecagon, calculated using circumradius. Inradius of Hendecagon is denoted by ri symbol.

How to calculate Inradius of Hendecagon given Circumradius using this online calculator? To use this online calculator for Inradius of Hendecagon given Circumradius, enter Circumradius of Hendecagon (rc) and hit the calculate button. Here is how the Inradius of Hendecagon given Circumradius calculation can be explained with given input values -> 8.635437 = (sin(pi/11)*9)/tan(pi/11).

FAQ

What is Inradius of Hendecagon given Circumradius?
The inradius of Hendecagon given Circumradius formula is defined as the straight line connecting the incenter of the Hendecagon and any point on the circle that touches all edges of the Hendecagon, calculated using circumradius and is represented as ri = (sin(pi/11)*rc)/tan(pi/11) or Inradius of Hendecagon = (sin(pi/11)*Circumradius of Hendecagon)/tan(pi/11). The Circumradius of Hendecagon is the radius of a circumcircle touching each of the vertices of Hendecagon.
How to calculate Inradius of Hendecagon given Circumradius?
The inradius of Hendecagon given Circumradius formula is defined as the straight line connecting the incenter of the Hendecagon and any point on the circle that touches all edges of the Hendecagon, calculated using circumradius is calculated using Inradius of Hendecagon = (sin(pi/11)*Circumradius of Hendecagon)/tan(pi/11). To calculate Inradius of Hendecagon given Circumradius, you need Circumradius of Hendecagon (rc). With our tool, you need to enter the respective value for Circumradius of Hendecagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Inradius of Hendecagon?
In this formula, Inradius of Hendecagon uses Circumradius of Hendecagon. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • Inradius of Hendecagon = (Height of Hendecagon*tan(pi/22))/(tan(pi/11))
  • Inradius of Hendecagon = (Perimeter of Hendecagon)/(22*tan(pi/11))
  • Inradius of Hendecagon = Side of Hendecagon/(2*tan(pi/11))
  • Inradius of Hendecagon = sqrt(Area of Hendecagon*(4*tan(pi/11))/11)/(2*tan(pi/11))
  • Inradius of Hendecagon = (((Diagonal across Five Sides of Hendecagon*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11))
  • Inradius of Hendecagon = (((Diagonal across Four Sides of Hendecagon*sin(pi/11))/sin((4*pi)/11)))/(2*tan(pi/11))
  • Inradius of Hendecagon = (((Diagonal across Three Sides of Hendecagon*sin(pi/11))/sin((3*pi)/11)))/(2*tan(pi/11))
  • Inradius of Hendecagon = (((Diagonal across Two Sides of Hendecagon*sin(pi/11))/sin((2*pi)/11)))/(2*tan(pi/11))
  • Inradius of Hendecagon = (((Width of hendecagon*sin(pi/11))/sin((5*pi)/11)))/(2*tan(pi/11))
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