Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides Calculator

✖Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.ⓘ Diagonal across Four Sides of Hexadecagon [d₄]

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

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Formula

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Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides

Formula

`"d"_{"3"} = sqrt(2)*"d"_{"4"}*sin((3*pi)/16)`

Example

`"14.14251m"=sqrt(2)*"18m"*sin((3*pi)/16)`

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Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Three Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/16)
d₃ = sqrt(2)*d₄*sin((3*pi)/16)
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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Diagonal across Three Sides of Hexadecagon - (Measured in Meter) - Diagonal across Three Sides of Hexadecagon is the straight line joining two non-adjacent vertices across the three sides of the Hexadecagon.
Diagonal across Four Sides of Hexadecagon - (Measured in Meter) - Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.

STEP 1: Convert Input(s) to Base Unit

Diagonal across Four Sides of Hexadecagon: 18 Meter --> 18 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d₃ = sqrt(2)*d₄*sin((3*pi)/16) --> sqrt(2)*18*sin((3*pi)/16)

Evaluating ... ...

d₃ = 14.1425092509678

STEP 3: Convert Result to Output's Unit

14.1425092509678 Meter --> No Conversion Required

FINAL ANSWER

14.1425092509678 ≈ 14.14251 Meter <-- Diagonal across Three Sides of Hexadecagon

(Calculation completed in 00.004 seconds)

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< 12 Diagonal of Hexadecagon across Three Sides Calculators

Diagonal of Hexadecagon across Three Sides given Circumradius

Go Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))

Diagonal of Hexadecagon across Three Sides given Inradius

Go Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))

Diagonal of Hexadecagon across Three Sides given Area

Go Diagonal across Three Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16)

Diagonal of Hexadecagon across Three Sides given Diagonal across Seven Sides

Go Diagonal across Three Sides of Hexadecagon = Diagonal across Seven Sides of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)

Diagonal of Hexadecagon across Three Sides given Diagonal across Five Sides

Go Diagonal across Three Sides of Hexadecagon = Diagonal across Five Sides of Hexadecagon*sin((3*pi)/16)/sin((5*pi)/16)

Diagonal of Hexadecagon across Three Sides given Diagonal across Six Sides

Go Diagonal across Three Sides of Hexadecagon = Diagonal across Six Sides of Hexadecagon*sin((3*pi)/16)/sin((3*pi)/8)

Diagonal of Hexadecagon across Three Sides given Diagonal across Two Sides

Go Diagonal across Three Sides of Hexadecagon = Diagonal across Two Sides of Hexadecagon*sin((3*pi)/16)/sin(pi/8)

Diagonal of Hexadecagon across Three Sides given Perimeter

Go Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Perimeter of Hexadecagon/16

Diagonal of Hexadecagon across Three Sides given Height

Go Diagonal across Three Sides of Hexadecagon = Height of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)

Diagonal of Hexadecagon across Three Sides

Go Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Side of Hexadecagon

Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides

Go Diagonal across Three Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/16)

Diagonal of Hexadecagon across Three Sides given Diagonal across Eight Sides

Go Diagonal across Three Sides of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin((3*pi)/16)

Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides Formula

Diagonal across Three Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/16)
d₃ = sqrt(2)*d₄*sin((3*pi)/16)

What is Hexadecagon?

A Hexadecagon is a 16-sided polygon, in which all angles are equal and all sides are congruent. Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees. Hexadecagons are sometimes used in art and architecture.

How to Calculate Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides?

Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides calculator uses Diagonal across Three Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/16) to calculate the Diagonal across Three Sides of Hexadecagon, The Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using diagonal across four sides. Diagonal across Three Sides of Hexadecagon is denoted by d₃ symbol.

How to calculate Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides using this online calculator? To use this online calculator for Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides, enter Diagonal across Four Sides of Hexadecagon (d₄) and hit the calculate button. Here is how the Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides calculation can be explained with given input values -> 14.14251 = sqrt(2)*18*sin((3*pi)/16).

FAQ

What is Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides?

The Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using diagonal across four sides and is represented as d₃ = sqrt(2)*d₄*sin((3*pi)/16) or Diagonal across Three Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/16). Diagonal across four sides of Hexadecagon is the straight line joining two non-adjacent vertices across four sides of Hexadecagon.

How to calculate Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides?

The Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using diagonal across four sides is calculated using Diagonal across Three Sides of Hexadecagon = sqrt(2)*Diagonal across Four Sides of Hexadecagon*sin((3*pi)/16). To calculate Diagonal of Hexadecagon across Three Sides given Diagonal across Four Sides, you need Diagonal across Four Sides of Hexadecagon (d₄). With our tool, you need to enter the respective value for Diagonal across Four Sides of Hexadecagon 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 Hexadecagon?

In this formula, Diagonal across Three Sides of Hexadecagon uses Diagonal across Four Sides of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -

Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Side of Hexadecagon
Diagonal across Three Sides of Hexadecagon = Height of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)
Diagonal across Three Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16)
Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Perimeter of Hexadecagon/16
Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2))))
Diagonal across Three Sides of Hexadecagon = Diagonal across Two Sides of Hexadecagon*sin((3*pi)/16)/sin(pi/8)
Diagonal across Three Sides of Hexadecagon = Diagonal across Five Sides of Hexadecagon*sin((3*pi)/16)/sin((5*pi)/16)
Diagonal across Three Sides of Hexadecagon = Diagonal across Six Sides of Hexadecagon*sin((3*pi)/16)/sin((3*pi)/8)
Diagonal across Three Sides of Hexadecagon = Diagonal across Seven Sides of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)
Diagonal across Three Sides of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin((3*pi)/16)

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