Diagonal of Nonagon across Four Sides given Height Calculator

✖Diagonal across Four Sides of Nonagon is the straight line joining two non-adjacent vertices which are across four sides of the Nonagon.ⓘ Diagonal of Nonagon across Four Sides given Height [d₄]

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Formula

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Diagonal of Nonagon across Four Sides given Height

Formula

`"d"_{"4"} = sin(4*pi/9)*"h"/(cos(pi/18))^2`

Example

`"22.33939m"=sin(4*pi/9)*"22m"/(cos(pi/18))^2`

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Diagonal of Nonagon across Four Sides given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Four Sides of Nonagon = sin(4*pi/9)*Height of Nonagon/(cos(pi/18))^2
d₄ = sin(4*pi/9)*h/(cos(pi/18))^2
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 Four Sides of Nonagon - (Measured in Meter) - Diagonal across Four Sides of Nonagon is the straight line joining two non-adjacent vertices which are across four sides of the Nonagon.
Height of Nonagon - (Measured in Meter) - Height of Nonagon is the length of a perpendicular line drawn from one vertex to the opposite side.

STEP 1: Convert Input(s) to Base Unit

Height of Nonagon: 22 Meter --> 22 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₄ = sin(4*pi/9)*h/(cos(pi/18))^2 --> sin(4*pi/9)*22/(cos(pi/18))^2

Evaluating ... ...

d₄ = 22.3393854614864

STEP 3: Convert Result to Output's Unit

22.3393854614864 Meter --> No Conversion Required

FINAL ANSWER

22.3393854614864 ≈ 22.33939 Meter <-- Diagonal across Four Sides of Nonagon

(Calculation completed in 00.004 seconds)

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< 6 Diagonal of Nonagon across Four sides Calculators

Diagonal of Nonagon across Four Sides given Area

Go Diagonal across Four Sides of Nonagon = sqrt(16*sin(4*pi/9)*cos(2*pi/9)*Area of Nonagon/9)

Diagonal of Nonagon across Four Sides given Perimeter

Go Diagonal across Four Sides of Nonagon = Perimeter of Nonagon/9*(sin(4*pi/9)/sin(pi/9))

Diagonal of Nonagon across Four Sides given Height

Go Diagonal across Four Sides of Nonagon = sin(4*pi/9)*Height of Nonagon/(cos(pi/18))^2

Diagonal of Nonagon across Four Sides given Inradius

Go Diagonal across Four Sides of Nonagon = tan(pi/9)*Inradius of Nonagon/sin(pi/18)

Diagonal of Nonagon across Four Sides

Go Diagonal across Four Sides of Nonagon = Side of Nonagon*(sin(4*pi/9)/sin(pi/9))

Diagonal of Nonagon across Four Sides given Circumradius

Go Diagonal across Four Sides of Nonagon = 2*Circumradius of Nonagon*sin(4*pi/9)

Diagonal of Nonagon across Four Sides given Height Formula

Diagonal across Four Sides of Nonagon = sin(4*pi/9)*Height of Nonagon/(cos(pi/18))^2
d₄ = sin(4*pi/9)*h/(cos(pi/18))^2

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 Four Sides given Height?

Diagonal of Nonagon across Four Sides given Height calculator uses Diagonal across Four Sides of Nonagon = sin(4*pi/9)*Height of Nonagon/(cos(pi/18))^2 to calculate the Diagonal across Four Sides of Nonagon, The Diagonal of Nonagon across Four Sides given Height formula is defined as the straight line connecting two vertices across four sides of Nonagon, calculated using height. Diagonal across Four Sides of Nonagon is denoted by d₄ symbol.

How to calculate Diagonal of Nonagon across Four Sides given Height using this online calculator? To use this online calculator for Diagonal of Nonagon across Four Sides given Height, enter Height of Nonagon (h) and hit the calculate button. Here is how the Diagonal of Nonagon across Four Sides given Height calculation can be explained with given input values -> 22.33939 = sin(4*pi/9)*22/(cos(pi/18))^2.

FAQ

What is Diagonal of Nonagon across Four Sides given Height?

The Diagonal of Nonagon across Four Sides given Height formula is defined as the straight line connecting two vertices across four sides of Nonagon, calculated using height and is represented as d₄ = sin(4*pi/9)*h/(cos(pi/18))^2 or Diagonal across Four Sides of Nonagon = sin(4*pi/9)*Height of Nonagon/(cos(pi/18))^2. Height of Nonagon is the length of a perpendicular line drawn from one vertex to the opposite side.

How to calculate Diagonal of Nonagon across Four Sides given Height?

The Diagonal of Nonagon across Four Sides given Height formula is defined as the straight line connecting two vertices across four sides of Nonagon, calculated using height is calculated using Diagonal across Four Sides of Nonagon = sin(4*pi/9)*Height of Nonagon/(cos(pi/18))^2. To calculate Diagonal of Nonagon across Four Sides given Height, you need Height of Nonagon (h). With our tool, you need to enter the respective value for Height 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 Four Sides of Nonagon?

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

Diagonal across Four Sides of Nonagon = 2*Circumradius of Nonagon*sin(4*pi/9)
Diagonal across Four Sides of Nonagon = Perimeter of Nonagon/9*(sin(4*pi/9)/sin(pi/9))
Diagonal across Four Sides of Nonagon = Side of Nonagon*(sin(4*pi/9)/sin(pi/9))
Diagonal across Four Sides of Nonagon = sqrt(16*sin(4*pi/9)*cos(2*pi/9)*Area of Nonagon/9)
Diagonal across Four Sides of Nonagon = tan(pi/9)*Inradius of Nonagon/sin(pi/18)

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