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Diagonal of Hexadecagon across Five Sides given Circumradius Formula

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Diagonal across Five Sides of Hexadecagon is the straight line joining two non-adjacent vertices across five sides of Hexadecagon. Check FAQs

d 5 = \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{r c}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

d₅ - Diagonal across Five Sides of Hexadecagon?r_c - Circumradius of Hexadecagon?π - Archimedes' constant?

Diagonal of Hexadecagon across Five Sides given Circumradius Example

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Here is how the Diagonal of Hexadecagon across Five Sides given Circumradius equation looks like with Values.

Here is how the Diagonal of Hexadecagon across Five Sides given Circumradius equation looks like with Units.

Here is how the Diagonal of Hexadecagon across Five Sides given Circumradius equation looks like.

21.6182 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

21.6182m = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

21.6182 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

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Diagonal of Hexadecagon across Five Sides given Circumradius Solution

Follow our step by step solution on how to calculate Diagonal of Hexadecagon across Five Sides given Circumradius?

FIRST Step Consider the formula

d 5 = \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{r c}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

Next Step Substitute values of Variables

∴

d 5 = \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

Next Step Substitute values of Constants

∴

d 5 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{13m}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

Next Step Prepare to Evaluate

∴

d 5 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{13}{\sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}}

Next Step Evaluate

∴

d 5 = 21.6182099198662m

LAST Step Rounding Answer

∴

d 5 = 21.6182m

Diagonal of Hexadecagon across Five Sides given Circumradius Formula Elements

Variables

Constants

Functions

Diagonal across Five Sides of Hexadecagon

Diagonal across Five Sides of Hexadecagon is the straight line joining two non-adjacent vertices across five sides of Hexadecagon.

Symbol: d₅

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Five Sides of Hexadecagon

Circumradius of Hexadecagon

Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius of Hexadecagon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Diagonal across Five Sides of Hexadecagon

Go Diagonal of Hexadecagon across Five Sides

d 5 = \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot S

Go Diagonal of Hexadecagon across Five Sides given Height

d 5 = h \cdot \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{7 \cdot π}{16})}

Go Diagonal of Hexadecagon across Five Sides given Area

d 5 = \sqrt{\frac{A}{4 \cdot \cot (\frac{π}{16})}} \cdot \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{π}{16})}

Go Diagonal of Hexadecagon across Five Sides given Perimeter

d 5 = \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{P}{16}

How to Evaluate Diagonal of Hexadecagon across Five Sides given Circumradius?

Diagonal of Hexadecagon across Five Sides given Circumradius evaluator uses Diagonal across Five Sides of Hexadecagon = sin((5*pi)/16)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)) to evaluate the Diagonal across Five Sides of Hexadecagon, The Diagonal of Hexadecagon across Five Sides given Circumradius formula is defined as the straight line connecting two non-adjacent vertices across five sides of Hexadecagon, calculated using circumradius. Diagonal across Five Sides of Hexadecagon is denoted by d₅ symbol.

How to evaluate Diagonal of Hexadecagon across Five Sides given Circumradius using this online evaluator? To use this online evaluator for Diagonal of Hexadecagon across Five Sides given Circumradius, enter Circumradius of Hexadecagon (r_c) and hit the calculate button.

FAQs on Diagonal of Hexadecagon across Five Sides given Circumradius

What is the formula to find Diagonal of Hexadecagon across Five Sides given Circumradius?

The formula of Diagonal of Hexadecagon across Five Sides given Circumradius is expressed as Diagonal across Five Sides of Hexadecagon = sin((5*pi)/16)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)). Here is an example- 21.61821 = sin((5*pi)/16)/sin(pi/16)*13/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)).

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

With Circumradius of Hexadecagon (r_c) we can find Diagonal of Hexadecagon across Five Sides given Circumradius using the formula - Diagonal across Five Sides of Hexadecagon = sin((5*pi)/16)/sin(pi/16)*Circumradius of Hexadecagon/(sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Diagonal across Five Sides of Hexadecagon?

Here are the different ways to Calculate Diagonal across Five Sides of Hexadecagon-

Diagonal across Five Sides of Hexadecagon=sin((5*pi)/16)/sin(pi/16)*Side of Hexadecagon
Diagonal across Five Sides of Hexadecagon=Height of Hexadecagon*sin((5*pi)/16)/sin((7*pi)/16)
Diagonal across Five Sides of Hexadecagon=sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((5*pi)/16)/sin(pi/16)

Can the Diagonal of Hexadecagon across Five Sides given Circumradius be negative?

No, the Diagonal of Hexadecagon across Five Sides given Circumradius, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Hexadecagon across Five Sides given Circumradius?

Diagonal of Hexadecagon across Five Sides given Circumradius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diagonal of Hexadecagon across Five Sides given Circumradius can be measured.

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