Diagonal of Hexadecagon across Three Sides given Circumradius Calculator

✖Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.ⓘ Circumradius of Hexadecagon [r_c]

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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 Circumradius [d₃]

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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)*r_c/(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 - 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.
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)*r_c/(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

FINAL ANSWER

14.4448260585097 ≈ 14.44483 Meter <-- Diagonal across Three Sides of Hexadecagon

(Calculation completed in 00.012 seconds)

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< Diagonal of Hexadecagon across Three Sides Calculators

Diagonal of Hexadecagon across Three Sides given Area

LaTeX 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 Perimeter

LaTeX 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

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

Diagonal of Hexadecagon across Three Sides

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

Diagonal of Hexadecagon across Three Sides given Circumradius Formula

LaTeX Go

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?

Diagonal of Hexadecagon across Three Sides given Circumradius calculator uses 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)) to calculate the Diagonal across Three Sides of Hexadecagon, The Diagonal of Hexadecagon across Three Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the circumradius. Diagonal across Three Sides of Hexadecagon is denoted by d₃ symbol.

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 (r_c) 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?

The Diagonal of Hexadecagon across Three Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the circumradius and is represented as d₃ = sin((3*pi)/16)/sin(pi/16)*r_c/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) or 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)). Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.

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

The Diagonal of Hexadecagon across Three Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the circumradius is calculated using 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)). To calculate Diagonal of Hexadecagon across Three Sides given Circumradius, you need Circumradius of Hexadecagon (r_c). 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 Three Sides of Hexadecagon?

In this formula, Diagonal across Three Sides of Hexadecagon uses Circumradius of Hexadecagon. We can use 3 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)

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