Diagonal of Nonagon across Three Sides given Inradius Calculator

✖Diagonal across Three Sides of Nonagon is the straight line joining two non-adjacent vertices which is across three sides of the Nonagon.ⓘ Diagonal of Nonagon across Three Sides given Inradius [d₃]

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Formula

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Diagonal of Nonagon across Three Sides given Inradius

Formula

`"d"_{"3"} = 2*"r"_{"i"}*sin(3*pi/9)/cos(pi/9)`

Example

`"20.27531m"=2*"11m"*sin(3*pi/9)/cos(pi/9)`

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Diagonal of Nonagon across Three Sides given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Three Sides of Nonagon = 2*Inradius of Nonagon*sin(3*pi/9)/cos(pi/9)
d₃ = 2*r_i*sin(3*pi/9)/cos(pi/9)
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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Diagonal across Three Sides of Nonagon - (Measured in Meter) - Diagonal across Three Sides of Nonagon is the straight line joining two non-adjacent vertices which is across three sides of the Nonagon.
Inradius of Nonagon - (Measured in Meter) - Inradius of Nonagon is defined as the radius of the circle which is inscribed inside the Nonagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Nonagon: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₃ = 2*r_i*sin(3*pi/9)/cos(pi/9) --> 2*11*sin(3*pi/9)/cos(pi/9)

Evaluating ... ...

d₃ = 20.2753096723513

STEP 3: Convert Result to Output's Unit

20.2753096723513 Meter --> No Conversion Required

FINAL ANSWER

20.2753096723513 ≈ 20.27531 Meter <-- Diagonal across Three Sides of Nonagon

(Calculation completed in 00.004 seconds)

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< 6 Diagonal of Nonagon across Three Sides Calculators

Diagonal of Nonagon across Three Sides given Area

Go Diagonal across Three Sides of Nonagon = sqrt(4*sin(3*pi/9)*sin(3*pi/9)*Area of Nonagon/(9*cos(pi/9)*sin(pi/9)))

Diagonal of Nonagon across Three Sides given Height

Go Diagonal across Three Sides of Nonagon = 2*Height of Nonagon*sin(3*pi/9)*tan(pi/18)/sin(pi/9)

Diagonal of Nonagon across Three Sides given Perimeter

Go Diagonal across Three Sides of Nonagon = Perimeter of Nonagon/9*(sin(3*pi/9)/sin(pi/9))

Diagonal of Nonagon across Three Sides given Inradius

Go Diagonal across Three Sides of Nonagon = 2*Inradius of Nonagon*sin(3*pi/9)/cos(pi/9)

Diagonal of Nonagon across Three Sides

Go Diagonal across Three Sides of Nonagon = Side of Nonagon*(sin(3*pi/9)/sin(pi/9))

Diagonal of Nonagon across Three Sides given Circumradius

Go Diagonal across Three Sides of Nonagon = 2*Circumradius of Nonagon*sin(3*pi/9)

Diagonal of Nonagon across Three Sides given Inradius Formula

Diagonal across Three Sides of Nonagon = 2*Inradius of Nonagon*sin(3*pi/9)/cos(pi/9)
d₃ = 2*r_i*sin(3*pi/9)/cos(pi/9)

What is Nonagon?

A Nonagon is a polygon with nine sides and nine angles. The term ‘nonagon’ is a hybrid of the Latin word ‘nonus’ meaning nine and the Greek word ‘gon’ meaning sides. It is also known as ‘enneagon’, derived from the Greek word ‘enneagonon’, also meaning nine.

How to Calculate Diagonal of Nonagon across Three Sides given Inradius?

Diagonal of Nonagon across Three Sides given Inradius calculator uses Diagonal across Three Sides of Nonagon = 2*Inradius of Nonagon*sin(3*pi/9)/cos(pi/9) to calculate the Diagonal across Three Sides of Nonagon, The Diagonal of Nonagon across Three Sides given Inradius formula is defined as a straight line connecting two vertices across three sides of Nonagon, calculated using inradius. Diagonal across Three Sides of Nonagon is denoted by d₃ symbol.

How to calculate Diagonal of Nonagon across Three Sides given Inradius using this online calculator? To use this online calculator for Diagonal of Nonagon across Three Sides given Inradius, enter Inradius of Nonagon (r_i) and hit the calculate button. Here is how the Diagonal of Nonagon across Three Sides given Inradius calculation can be explained with given input values -> 20.27531 = 2*11*sin(3*pi/9)/cos(pi/9).

FAQ

What is Diagonal of Nonagon across Three Sides given Inradius?

The Diagonal of Nonagon across Three Sides given Inradius formula is defined as a straight line connecting two vertices across three sides of Nonagon, calculated using inradius and is represented as d₃ = 2*r_i*sin(3*pi/9)/cos(pi/9) or Diagonal across Three Sides of Nonagon = 2*Inradius of Nonagon*sin(3*pi/9)/cos(pi/9). Inradius of Nonagon is defined as the radius of the circle which is inscribed inside the Nonagon.

How to calculate Diagonal of Nonagon across Three Sides given Inradius?

The Diagonal of Nonagon across Three Sides given Inradius formula is defined as a straight line connecting two vertices across three sides of Nonagon, calculated using inradius is calculated using Diagonal across Three Sides of Nonagon = 2*Inradius of Nonagon*sin(3*pi/9)/cos(pi/9). To calculate Diagonal of Nonagon across Three Sides given Inradius, you need Inradius of Nonagon (r_i). With our tool, you need to enter the respective value for Inradius of Nonagon 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 Three Sides of Nonagon?

In this formula, Diagonal across Three Sides of Nonagon uses Inradius of Nonagon. We can use 5 other way(s) to calculate the same, which is/are as follows -

Diagonal across Three Sides of Nonagon = 2*Circumradius of Nonagon*sin(3*pi/9)
Diagonal across Three Sides of Nonagon = Perimeter of Nonagon/9*(sin(3*pi/9)/sin(pi/9))
Diagonal across Three Sides of Nonagon = Side of Nonagon*(sin(3*pi/9)/sin(pi/9))
Diagonal across Three Sides of Nonagon = sqrt(4*sin(3*pi/9)*sin(3*pi/9)*Area of Nonagon/(9*cos(pi/9)*sin(pi/9)))
Diagonal across Three Sides of Nonagon = 2*Height of Nonagon*sin(3*pi/9)*tan(pi/18)/sin(pi/9)

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