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Inradius of Hexadecagon given Diagonal across Five Sides Formula

GoInradius of Hexadecagon Formula

GoInradius of Hexadecagon given Diagonal across Seven Sides Formula

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Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon. Check FAQs

r i = \frac{d 5 \cdot \sin (\frac{π}{16})}{\sin (\frac{5 \cdot π}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

r_i - Inradius of Hexadecagon?d₅ - Diagonal across Five Sides of Hexadecagon?π - Archimedes' constant?

Inradius of Hexadecagon given Diagonal across Five Sides Example

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

12.3856 = \frac{21 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

12.3856m = \frac{21m \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

12.3856 = \frac{21 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

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Inradius of Hexadecagon given Diagonal across Five Sides Solution

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

FIRST Step Consider the formula

r i = \frac{d 5 \cdot \sin (\frac{π}{16})}{\sin (\frac{5 \cdot π}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Next Step Substitute values of Variables

∴

r i = \frac{21m \cdot \sin (\frac{π}{16})}{\sin (\frac{5 \cdot π}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Next Step Substitute values of Constants

∴

r i = \frac{21m \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Next Step Prepare to Evaluate

∴

r i = \frac{21 \cdot \sin (\frac{3.1416}{16})}{\sin (\frac{5 \cdot 3.1416}{16})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Next Step Evaluate

∴

r i = 12.3855944845844m

LAST Step Rounding Answer

∴

r i = 12.3856m

Inradius of Hexadecagon given Diagonal across Five Sides Formula Elements

Variables

Constants

Functions

Inradius of Hexadecagon

Inradius of Hexadecagon is defined as the radius of the circle which is inscribed inside the Hexadecagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius 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 Inradius of Hexadecagon

Go Inradius of Hexadecagon

r i = (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2}) \cdot S

Go Inradius of Hexadecagon given Diagonal across Seven Sides

r i = \frac{d 7}{2}

Go Inradius of Hexadecagon given Diagonal across Eight Sides

r i = d 8 \cdot \sin (\frac{π}{16}) \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

Go Inradius of Hexadecagon given Diagonal across Six Sides

r i = \frac{d 6 \cdot \sin (\frac{π}{16})}{\sin (\frac{3 \cdot π}{8})} \cdot (\frac{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}{2})

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

Inradius of Hexadecagon given Diagonal across Five Sides evaluator uses Inradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2) to evaluate the Inradius of Hexadecagon, The Inradius of Hexadecagon given Diagonal across Five Sides formula is defined as a straight line connecting the in-center and any point on the circle that touches all sides of the Hexadecagon, calculated using a diagonal across five sides. Inradius of Hexadecagon is denoted by r_i symbol.

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

FAQs on Inradius of Hexadecagon given Diagonal across Five Sides

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

The formula of Inradius of Hexadecagon given Diagonal across Five Sides is expressed as Inradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2). Here is an example- 12.38559 = (21*sin(pi/16))/sin((5*pi)/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2).

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

With Diagonal across Five Sides of Hexadecagon (d₅) we can find Inradius of Hexadecagon given Diagonal across Five Sides using the formula - Inradius of Hexadecagon = (Diagonal across Five Sides of Hexadecagon*sin(pi/16))/sin((5*pi)/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Inradius of Hexadecagon?

Here are the different ways to Calculate Inradius of Hexadecagon-

Inradius of Hexadecagon=((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)*Side of Hexadecagon
Inradius of Hexadecagon=Diagonal across Seven Sides of Hexadecagon/2
Inradius of Hexadecagon=Diagonal across Eight Sides of Hexadecagon*sin(pi/16)*((1+sqrt(2)+sqrt(2*(2+sqrt(2))))/2)

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

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

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

Inradius 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 Inradius of Hexadecagon given Diagonal across Five Sides can be measured.

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