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Diagonal of Hexadecagon across Five Sides given Inradius Formula

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GoDiagonal of Hexadecagon across Five Sides given Height 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{2 \cdot r i}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

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

Diagonal of Hexadecagon across Five Sides given Inradius Example

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

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

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

20.3462 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{2 \cdot 12}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

20.3462m = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{2 \cdot 12m}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

20.3462 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{2 \cdot 12}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

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Diagonal of Hexadecagon across Five Sides given Inradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d 5 = \frac{\sin (\frac{5 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{2 \cdot 12m}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

Next Step Substitute values of Constants

∴

d 5 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{2 \cdot 12m}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

Next Step Prepare to Evaluate

∴

d 5 = \frac{\sin (\frac{5 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{2 \cdot 12}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

Next Step Evaluate

∴

d 5 = 20.3462175605418m

LAST Step Rounding Answer

∴

d 5 = 20.3462m

Diagonal of Hexadecagon across Five Sides given Inradius 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

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

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 Inradius?

Diagonal of Hexadecagon across Five Sides given Inradius evaluator uses Diagonal across Five Sides of Hexadecagon = sin((5*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) to evaluate the Diagonal across Five Sides of Hexadecagon, The Diagonal of Hexadecagon across Five Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across five sides of Hexadecagon, calculated using inradius. Diagonal across Five Sides of Hexadecagon is denoted by d₅ symbol.

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

FAQs on Diagonal of Hexadecagon across Five Sides given Inradius

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

The formula of Diagonal of Hexadecagon across Five Sides given Inradius is expressed as Diagonal across Five Sides of Hexadecagon = sin((5*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))). Here is an example- 20.34622 = sin((5*pi)/16)/sin(pi/16)*(2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))).

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

With Inradius of Hexadecagon (r_i) we can find Diagonal of Hexadecagon across Five Sides given Inradius using the formula - Diagonal across Five Sides of Hexadecagon = sin((5*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(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 Inradius be negative?

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

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

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

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