## Diagonal of Hexadecagon across Three Sides given Circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
d3 = sin(3*pi/16)/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 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.
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
d3 = sin(3*pi/16)/sin(pi/16)*rc/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) --> sin(3*pi/16)/sin(pi/16)*13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
Evaluating ... ...
d3 = 14.4448260585097
STEP 3: Convert Result to Output's Unit
14.4448260585097 Meter --> No Conversion Required
14.4448260585097 Meter <-- Diagonal across Three Sides of Hexadecagon
(Calculation completed in 00.010 seconds)
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## < 10+ Diagonal of Hexadecagon across Three Sides Calculators

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

## Diagonal of Hexadecagon across Three Sides given Circumradius Formula

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))
d3 = sin(3*pi/16)/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 Three Sides given Circumradius?

How to calculate Diagonal of Hexadecagon across Three Sides given Circumradius using this online calculator? To use this online calculator for Diagonal of Hexadecagon across Three Sides given Circumradius, enter Circumradius of Hexadecagon (rc) and hit the calculate button. Here is how the Diagonal of Hexadecagon across Three Sides given Circumradius calculation can be explained with given input values -> 14.44483 = sin(3*pi/16)/sin(pi/16)*13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)).

### FAQ

What is Diagonal of Hexadecagon across Three Sides given Circumradius?
How to calculate Diagonal of Hexadecagon across Three Sides given Circumradius?
How many ways are there to calculate Diagonal across Three Sides of Hexadecagon?
In this formula, Diagonal across Three 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 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))*Inradius of Hexadecagon/((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)
• Diagonal across Three Sides of Hexadecagon = ((sin(3*pi/16))/(sin(pi/16)))*Diagonal across Two Sides of Hexadecagon*((sin(pi/16))/(sin(pi/8)))
• Diagonal across Three Sides of Hexadecagon = ((sin(3*pi/16))/(sin(pi/16)))*(Diagonal across Four Sides of Hexadecagon)/((sqrt(2))/2/(sin(pi/16)))
• Diagonal across Three Sides of Hexadecagon = ((sin(3*pi/16))/(sin(pi/16)))*Diagonal across Five Sides of Hexadecagon*((sin(pi/16))/(sin(5*pi/16)))
• Diagonal across Three Sides of Hexadecagon = ((sin(3*pi/16))/(sin(pi/16)))*Diagonal across Six Sides of Hexadecagon*((sin(pi/16))/(sin(3*pi/8)))
• Diagonal across Three Sides of Hexadecagon = ((sin(3*pi/16))/(sin(pi/16)))*Diagonal across Seven Sides of Hexadecagon*((sin(pi/16))/(sin(7*pi/16)))
• Diagonal across Three Sides of Hexadecagon = ((sin(3*pi/16))/(sin(pi/16)))*Diagonal across Eight Sides of Hexadecagon*sin(pi/16)
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