Diagonal of Hexadecagon across Seven 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 Seven Sides of Hexadecagon is a straight line joining two non-adjacent vertices across seven sides of Hexadecagon.ⓘ Diagonal of Hexadecagon across Seven Sides given Circumradius [d₇]

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Diagonal of Hexadecagon across Seven Sides given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal across Seven Sides of Hexadecagon = sin((7*pi)/16)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))
d₇ = sin((7*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 Seven Sides of Hexadecagon - (Measured in Meter) - Diagonal across Seven Sides of Hexadecagon is a straight line joining two non-adjacent vertices across seven sides of 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

d₇ = sin((7*pi)/16)/sin(pi/16)*r_c/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) --> sin((7*pi)/16)/sin(pi/16)*13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))

Evaluating ... ...

d₇ = 25.500417290484

STEP 3: Convert Result to Output's Unit

25.500417290484 Meter --> No Conversion Required

FINAL ANSWER

25.500417290484 ≈ 25.50042 Meter <-- Diagonal across Seven Sides of Hexadecagon

(Calculation completed in 00.008 seconds)

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< Diagonal of Hexadecagon across Seven Sides Calculators

Diagonal of Hexadecagon across Seven Sides given Area

LaTeX Go Diagonal across Seven Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((7*pi)/16)/sin(pi/16)

Diagonal of Hexadecagon across Seven Sides given Perimeter

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

Diagonal of Hexadecagon across Seven Sides

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

Diagonal of Hexadecagon across Seven Sides given Inradius

LaTeX Go Diagonal across Seven Sides of Hexadecagon = 2*Inradius of Hexadecagon

Diagonal of Hexadecagon across Seven Sides given Circumradius Formula

LaTeX Go

What is a 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 Seven Sides given Circumradius?

Diagonal of Hexadecagon across Seven Sides given Circumradius calculator uses Diagonal across Seven Sides of Hexadecagon = sin((7*pi)/16)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) to calculate the Diagonal across Seven Sides of Hexadecagon, The Diagonal of Hexadecagon across Seven Sides given Circumradius formula is defined as as the straight line connecting two non-adjacent vertices across seven sides of Hexadecagon, calculated using circumradius. Diagonal across Seven Sides of Hexadecagon is denoted by d₇ symbol.

How to calculate Diagonal of Hexadecagon across Seven Sides given Circumradius using this online calculator? To use this online calculator for Diagonal of Hexadecagon across Seven Sides given Circumradius, enter Circumradius of Hexadecagon (r_c) and hit the calculate button. Here is how the Diagonal of Hexadecagon across Seven Sides given Circumradius calculation can be explained with given input values -> 25.50042 = sin((7*pi)/16)/sin(pi/16)*13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)).

FAQ

What is Diagonal of Hexadecagon across Seven Sides given Circumradius?

The Diagonal of Hexadecagon across Seven Sides given Circumradius formula is defined as as the straight line connecting two non-adjacent vertices across seven sides of Hexadecagon, calculated using circumradius and is represented as d₇ = sin((7*pi)/16)/sin(pi/16)*r_c/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) or Diagonal across Seven Sides of Hexadecagon = sin((7*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 Seven Sides given Circumradius?

The Diagonal of Hexadecagon across Seven Sides given Circumradius formula is defined as as the straight line connecting two non-adjacent vertices across seven sides of Hexadecagon, calculated using circumradius is calculated using Diagonal across Seven Sides of Hexadecagon = sin((7*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 Seven 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 Seven Sides of Hexadecagon?

In this formula, Diagonal across Seven 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 Seven Sides of Hexadecagon = sin((7*pi)/16)/sin(pi/16)*Side of Hexadecagon
Diagonal across Seven Sides of Hexadecagon = 2*Inradius of Hexadecagon
Diagonal across Seven Sides of Hexadecagon = sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((7*pi)/16)/sin(pi/16)

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