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Circumradius of Hexadecagon given Diagonal across Five Sides Formula

GoCircumradius of Hexadecagon given Diagonal across Eight Sides Formula

GoCircumradius of Hexadecagon Formula

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

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

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

Circumradius of Hexadecagon given Diagonal across Five Sides Example

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

12.6282 = \frac{21 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

12.6282m = \frac{21m \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

12.6282 = \frac{21 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

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Circumradius of Hexadecagon given Diagonal across Five Sides Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \frac{21m \cdot \sin (\frac{π}{16})}{\sin (\frac{5 \cdot π}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

Next Step Substitute values of Constants

∴

r c = \frac{21m \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

Next Step Prepare to Evaluate

∴

r c = \frac{21 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

Next Step Evaluate

∴

r c = 12.628242625636m

LAST Step Rounding Answer

∴

r c = 12.6282m

Circumradius of Hexadecagon given Diagonal across Five Sides Formula Elements

Variables

Constants

Functions

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

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

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 Circumradius of Hexadecagon

Go Circumradius of Hexadecagon given Diagonal across Eight Sides

r c = \frac{d 8}{2}

Go Circumradius of Hexadecagon

r c = \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}} \cdot S

Go Circumradius of Hexadecagon given Diagonal across Seven Sides

r c = \frac{d 7 \cdot \sin (\frac{π}{16})}{\sin (\frac{7 \cdot π}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

Go Circumradius of Hexadecagon given Diagonal across Six Sides

r c = \frac{d 6 \cdot \sin (\frac{π}{16})}{\sin (\frac{3 \cdot π}{8})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

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

Circumradius of Hexadecagon given Diagonal across Five Sides evaluator uses Circumradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2) to evaluate the Circumradius of Hexadecagon, The Circumradius of Hexadecagon given Diagonal across Five Sides formula is defined as the straight line connecting the circumcenter and any point on the circle that touches all the vertices of Hexadecagon, calculated using diagonal across five sides. Circumradius of Hexadecagon is denoted by r_c symbol.

How to evaluate Circumradius of Hexadecagon given Diagonal across Five Sides using this online evaluator? To use this online evaluator for Circumradius of Hexadecagon given Diagonal across Five Sides, enter Diagonal across Five Sides of Hexadecagon (d₅) and hit the calculate button.

FAQs on Circumradius of Hexadecagon given Diagonal across Five Sides

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

The formula of Circumradius of Hexadecagon given Diagonal across Five Sides is expressed as Circumradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2). Here is an example- 12.62824 = (21*sin(pi/16))/sin((5*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2).

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

With Diagonal across Five Sides of Hexadecagon (d₅) we can find Circumradius of Hexadecagon given Diagonal across Five Sides using the formula - Circumradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*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 Circumradius of Hexadecagon?

Here are the different ways to Calculate Circumradius of Hexadecagon-

Circumradius of Hexadecagon=Diagonal across Eight Sides of Hexadecagon/2
Circumradius of Hexadecagon=sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)*Side of Hexadecagon
Circumradius of Hexadecagon=(Diagonal across Seven Sides of Hexadecagon*sin(pi/16))/sin((7*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

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

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

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

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

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