Diagonal of Hexadecagon across Two Sides given Circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diagonal across Two Sides of Hexadecagon = (sin(pi/8)/sin(pi/16))*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
d2 = (sin(pi/8)/sin(pi/16))*rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Diagonal across Two Sides of Hexadecagon - (Measured in Meter) - Diagonal across two sides of Hexadecagon is the straight line joining two non-adjacent vertices across the two sides of the Hexadecagon.
Circumradius of Hexadecagon - (Measured in Meter) - Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
STEP 1: Convert Input(s) to Base Unit
Circumradius of Hexadecagon: 13 Meter --> 13 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d2 = (sin(pi/8)/sin(pi/16))*rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) --> (sin(pi/8)/sin(pi/16))*13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
Evaluating ... ...
d2 = 9.94976924149234
STEP 3: Convert Result to Output's Unit
9.94976924149234 Meter --> No Conversion Required
FINAL ANSWER
9.94976924149234 Meter <-- Diagonal across Two Sides of Hexadecagon
(Calculation completed in 00.011 seconds)

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10+ Diagonal of Hexadecagon across Two Sides Calculators

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

Diagonal of Hexadecagon across Two Sides given Circumradius Formula

Diagonal across Two Sides of Hexadecagon = (sin(pi/8)/sin(pi/16))*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
d2 = (sin(pi/8)/sin(pi/16))*rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))

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 Two Sides given Circumradius?

Diagonal of Hexadecagon across Two Sides given Circumradius calculator uses Diagonal across Two Sides of Hexadecagon = (sin(pi/8)/sin(pi/16))*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) to calculate the Diagonal across Two Sides of Hexadecagon, The Diagonal of Hexadecagon across Two Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across two sides of the Hexadecagon, calculated using circumradius. Diagonal across Two Sides of Hexadecagon is denoted by d2 symbol.

How to calculate Diagonal of Hexadecagon across Two Sides given Circumradius using this online calculator? To use this online calculator for Diagonal of Hexadecagon across Two Sides given Circumradius, enter Circumradius of Hexadecagon (rc) and hit the calculate button. Here is how the Diagonal of Hexadecagon across Two Sides given Circumradius calculation can be explained with given input values -> 9.949769 = (sin(pi/8)/sin(pi/16))*13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)).

FAQ

What is Diagonal of Hexadecagon across Two Sides given Circumradius?
The Diagonal of Hexadecagon across Two Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across two sides of the Hexadecagon, calculated using circumradius and is represented as d2 = (sin(pi/8)/sin(pi/16))*rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) or Diagonal across Two Sides of Hexadecagon = (sin(pi/8)/sin(pi/16))*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)). Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
How to calculate Diagonal of Hexadecagon across Two Sides given Circumradius?
The Diagonal of Hexadecagon across Two Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across two sides of the Hexadecagon, calculated using circumradius is calculated using Diagonal across Two Sides of Hexadecagon = (sin(pi/8)/sin(pi/16))*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)). To calculate Diagonal of Hexadecagon across Two Sides given Circumradius, you need Circumradius of Hexadecagon (rc). With our tool, you need to enter the respective value for Circumradius 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 Two Sides of Hexadecagon?
In this formula, Diagonal across Two Sides of Hexadecagon uses Circumradius of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Diagonal across Two Sides of Hexadecagon = ((sin(pi/8))/(sin(pi/16)))*(Side of Hexadecagon)
  • Diagonal across Two Sides of Hexadecagon = (Height of Hexadecagon)*(sin(pi/8)/sin(7*pi/16))
  • Diagonal across Two Sides of Hexadecagon = (sqrt(Area of Hexadecagon/(4*cot(pi/16))))* (sin(pi/8)/sin(pi/16))
  • Diagonal across Two Sides of Hexadecagon = (sin(pi/8)/sin(pi/16))*(Perimeter of Hexadecagon/16)
  • Diagonal across Two Sides of Hexadecagon = (sin(pi/8)/sin(pi/16))*Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)
  • Diagonal across Two Sides of Hexadecagon = ((sin(pi/8))/(sin(pi/16)))*Diagonal across Three Sides of Hexadecagon*((sin(pi/16))/(sin(3*pi/16)))
  • Diagonal across Two Sides of Hexadecagon = ((sin(pi/8))/(sin(pi/16)))*(Diagonal across Four Sides of Hexadecagon)/((sqrt(2))/2/(sin(pi/16)))
  • Diagonal across Two Sides of Hexadecagon = ((sin(pi/8))/(sin(pi/16)))*Diagonal across Five Sides of Hexadecagon*((sin(pi/16))/(sin(5*pi/16)))
  • Diagonal across Two Sides of Hexadecagon = ((sin(pi/8))/(sin(pi/16)))*Diagonal across Six Sides of Hexadecagon*((sin(pi/16))/(sin(3*pi/8)))
  • Diagonal across Two Sides of Hexadecagon = ((sin(pi/8))/(sin(pi/16)))*Diagonal across Seven Sides of Hexadecagon*((sin(pi/16))/(sin(7*pi/16)))
  • Diagonal across Two Sides of Hexadecagon = ((sin(pi/8))/(sin(pi/16)))*Diagonal across Eight Sides of Hexadecagon*sin(pi/16)
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