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Circumradius of Hexadecagon given Diagonal across Seven 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 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}}

r_c - Circumradius of Hexadecagon?d₇ - Diagonal across Seven Sides of Hexadecagon?π - Archimedes' constant?

Circumradius of Hexadecagon given Diagonal across Seven Sides Example

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

12.7449 = \frac{25 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{7 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

12.7449m = \frac{25m \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{7 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

12.7449 = \frac{25 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{7 \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 Seven Sides Solution

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

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

r c = \frac{25m \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}}

Next Step Substitute values of Constants

∴

r c = \frac{25m \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{7 \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{25 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{7 \cdot 3.1416}{16})} \cdot \sqrt{\frac{4 + (2 \cdot \sqrt{2}) + \sqrt{20 + (14 \cdot \sqrt{2})}}{2}}

Next Step Evaluate

∴

r c = 12.744889477604m

LAST Step Rounding Answer

∴

r c = 12.7449m

Circumradius of Hexadecagon given Diagonal across Seven 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 Seven Sides of Hexadecagon

Diagonal across Seven Sides of Hexadecagon is a straight line joining two non-adjacent vertices across seven sides of Hexadecagon.

Symbol: d₇

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Seven 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 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}}

Go Circumradius of Hexadecagon given Diagonal across Five Sides

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}}

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

Circumradius of Hexadecagon given Diagonal across Seven Sides evaluator uses 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) to evaluate the Circumradius of Hexadecagon, The Circumradius of Hexadecagon given Diagonal across Seven 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 seven sides. Circumradius of Hexadecagon is denoted by r_c symbol.

How to evaluate Circumradius of Hexadecagon given Diagonal across Seven Sides using this online evaluator? To use this online evaluator for Circumradius of Hexadecagon given Diagonal across Seven Sides, enter Diagonal across Seven Sides of Hexadecagon (d₇) and hit the calculate button.

FAQs on Circumradius of Hexadecagon given Diagonal across Seven Sides

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

The formula of Circumradius of Hexadecagon given Diagonal across Seven Sides is expressed as 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). Here is an example- 12.74489 = (25*sin(pi/16))/sin((7*pi)/16)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2).

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

With Diagonal across Seven Sides of Hexadecagon (d₇) we can find Circumradius of Hexadecagon given Diagonal across Seven Sides using the formula - 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). 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 Six Sides of Hexadecagon*sin(pi/16))/sin((3*pi)/8)*sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)

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

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

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

Circumradius of Hexadecagon given Diagonal across Seven 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 Seven Sides can be measured.

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