Diagonal of Hendecagon across Five Sides given Inradius Calculator

✖Diagonal across Five Sides of Hendecagon is a straight line joining two non-adjacent sides across five sides of the Hendecagon.ⓘ Diagonal of Hendecagon across Five Sides given Inradius [d₅]

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Formula

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Diagonal of Hendecagon across Five Sides given Inradius

Formula

`"d"_{"5"} = 2*tan(pi/11)*"r"_{"i"}*sin((5*pi)/11)/sin(pi/11)`

Example

`"16.50574m"=2*tan(pi/11)*"8m"*sin((5*pi)/11)/sin(pi/11)`

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Diagonal of Hendecagon across Five Sides given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Five Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((5*pi)/11)/sin(pi/11)
d₅ = 2*tan(pi/11)*r_i*sin((5*pi)/11)/sin(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

Diagonal across Five Sides of Hendecagon - (Measured in Meter) - Diagonal across Five Sides of Hendecagon is a straight line joining two non-adjacent sides across five sides of the Hendecagon.
Inradius of Hendecagon - (Measured in Meter) - The Inradius of Hendecagon is defined as the radius of the circle which is inscribed inside the Hendecagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Hendecagon: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₅ = 2*tan(pi/11)*r_i*sin((5*pi)/11)/sin(pi/11) --> 2*tan(pi/11)*8*sin((5*pi)/11)/sin(pi/11)

Evaluating ... ...

d₅ = 16.5057415797793

STEP 3: Convert Result to Output's Unit

16.5057415797793 Meter --> No Conversion Required

FINAL ANSWER

16.5057415797793 ≈ 16.50574 Meter <-- Diagonal across Five Sides of Hendecagon

(Calculation completed in 00.020 seconds)

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< 10+ Diagonal of Hendecagon across Five sides Calculators

Diagonal of Hendecagon across Five Sides given Area

Go Diagonal across Five Sides of Hendecagon = sqrt((4*Area of Hendecagon*tan(pi/11))/11)*sin((5*pi)/11)/sin(pi/11)

Diagonal of Hendecagon across Five Sides given Inradius

Go Diagonal across Five Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((5*pi)/11)/sin(pi/11)

Diagonal of Hendecagon across Five Sides given Height

Go Diagonal across Five Sides of Hendecagon = 2*tan(pi/22)*Height of Hendecagon*sin((5*pi)/11)/sin(pi/11)

Diagonal of Hendecagon across Five Sides given Diagonal across Four Sides

Go Diagonal across Five Sides of Hendecagon = Diagonal across Four Sides of Hendecagon*(sin((5*pi)/11))/(sin((4*pi)/11))

Diagonal of Hendecagon across Five Sides given Diagonal across Three Sides

Go Diagonal across Five Sides of Hendecagon = Diagonal across Three Sides of Hendecagon*sin((5*pi)/11)/(sin((3*pi)/11))

Diagonal of Hendecagon across Five Sides given Diagonal across Two Sides

Go Diagonal across Five Sides of Hendecagon = Diagonal across Two Sides of Hendecagon*(sin((5*pi)/11))/sin((2*pi)/11)

Diagonal of Hendecagon across Five Sides given Perimeter

Go Diagonal across Five Sides of Hendecagon = Perimeter of Hendecagon/11*sin((5*pi)/11)/sin(pi/11)

Diagonal of Hendecagon across Five Sides

Go Diagonal across Five Sides of Hendecagon = (Side of Hendecagon*sin((5*pi)/11))/sin(pi/11)

Diagonal of Hendecagon across Five Sides given Circumradius

Go Diagonal across Five Sides of Hendecagon = 2*Circumradius of Hendecagon*sin((5*pi)/11)

Diagonal of Hendecagon across Five Sides given Width

Go Diagonal across Five Sides of Hendecagon = Width of hendecagon/1

Diagonal of Hendecagon across Five Sides given Inradius Formula

Diagonal across Five Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((5*pi)/11)/sin(pi/11)
d₅ = 2*tan(pi/11)*r_i*sin((5*pi)/11)/sin(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 Diagonal of Hendecagon across Five Sides given Inradius?

Diagonal of Hendecagon across Five Sides given Inradius calculator uses Diagonal across Five Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((5*pi)/11)/sin(pi/11) to calculate the Diagonal across Five Sides of Hendecagon, The Diagonal of Hendecagon across Five Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across five sides of Hendecagon, calculated using inradius. Diagonal across Five Sides of Hendecagon is denoted by d₅ symbol.

How to calculate Diagonal of Hendecagon across Five Sides given Inradius using this online calculator? To use this online calculator for Diagonal of Hendecagon across Five Sides given Inradius, enter Inradius of Hendecagon (r_i) and hit the calculate button. Here is how the Diagonal of Hendecagon across Five Sides given Inradius calculation can be explained with given input values -> 16.50574 = 2*tan(pi/11)*8*sin((5*pi)/11)/sin(pi/11).

FAQ

What is Diagonal of Hendecagon across Five Sides given Inradius?

The Diagonal of Hendecagon across Five Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across five sides of Hendecagon, calculated using inradius and is represented as d₅ = 2*tan(pi/11)*r_i*sin((5*pi)/11)/sin(pi/11) or Diagonal across Five Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((5*pi)/11)/sin(pi/11). The Inradius of Hendecagon is defined as the radius of the circle which is inscribed inside the Hendecagon.

How to calculate Diagonal of Hendecagon across Five Sides given Inradius?

The Diagonal of Hendecagon across Five Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across five sides of Hendecagon, calculated using inradius is calculated using Diagonal across Five Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((5*pi)/11)/sin(pi/11). To calculate Diagonal of Hendecagon across Five Sides given Inradius, you need Inradius of Hendecagon (r_i). With our tool, you need to enter the respective value for Inradius 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 Diagonal across Five Sides of Hendecagon?

In this formula, Diagonal across Five Sides of Hendecagon uses Inradius of Hendecagon. We can use 9 other way(s) to calculate the same, which is/are as follows -

Diagonal across Five Sides of Hendecagon = (Side of Hendecagon*sin((5*pi)/11))/sin(pi/11)
Diagonal across Five Sides of Hendecagon = sqrt((4*Area of Hendecagon*tan(pi/11))/11)*sin((5*pi)/11)/sin(pi/11)
Diagonal across Five Sides of Hendecagon = 2*tan(pi/22)*Height of Hendecagon*sin((5*pi)/11)/sin(pi/11)
Diagonal across Five Sides of Hendecagon = Perimeter of Hendecagon/11*sin((5*pi)/11)/sin(pi/11)
Diagonal across Five Sides of Hendecagon = 2*Circumradius of Hendecagon*sin((5*pi)/11)
Diagonal across Five Sides of Hendecagon = Diagonal across Four Sides of Hendecagon*(sin((5*pi)/11))/(sin((4*pi)/11))
Diagonal across Five Sides of Hendecagon = Diagonal across Three Sides of Hendecagon*sin((5*pi)/11)/(sin((3*pi)/11))
Diagonal across Five Sides of Hendecagon = Diagonal across Two Sides of Hendecagon*(sin((5*pi)/11))/sin((2*pi)/11)
Diagonal across Five Sides of Hendecagon = Width of hendecagon/1

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