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Diagonal of Hexadecagon across Three Sides given Inradius Formula

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

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

d₃ - Diagonal across Three Sides of Hexadecagon?r_i - Inradius of Hexadecagon?π - Archimedes' constant?

Diagonal of Hexadecagon across Three Sides given Inradius Example

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

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

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

13.5949 = \frac{\sin (\frac{3 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{2 \cdot 12}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

13.5949m = \frac{\sin (\frac{3 \cdot 3.1416}{16})}{\sin (\frac{3.1416}{16})} \cdot \frac{2 \cdot 12m}{1 + \sqrt{2} + \sqrt{2 \cdot (2 + \sqrt{2})}}

13.5949 = \frac{\sin (\frac{3 \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 Three Sides given Inradius Solution

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

FIRST Step Consider the formula

d 3 = \frac{\sin (\frac{3 \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 3 = \frac{\sin (\frac{3 \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 3 = \frac{\sin (\frac{3 \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 3 = \frac{\sin (\frac{3 \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 3 = 13.5949079364125m

LAST Step Rounding Answer

∴

d 3 = 13.5949m

Diagonal of Hexadecagon across Three Sides given Inradius Formula Elements

Variables

Constants

Functions

Diagonal across Three Sides of Hexadecagon

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

Symbol: d₃

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Three 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 Three Sides of Hexadecagon

Go Diagonal of Hexadecagon across Three Sides

d 3 = \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot S

Go Diagonal of Hexadecagon across Three Sides given Height

d 3 = h \cdot \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{7 \cdot π}{16})}

Go Diagonal of Hexadecagon across Three Sides given Area

d 3 = \sqrt{\frac{A}{4 \cdot \cot (\frac{π}{16})}} \cdot \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})}

Go Diagonal of Hexadecagon across Three Sides given Perimeter

d 3 = \frac{\sin (\frac{3 \cdot π}{16})}{\sin (\frac{π}{16})} \cdot \frac{P}{16}

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

Diagonal of Hexadecagon across Three Sides given Inradius evaluator uses Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))) to evaluate the Diagonal across Three Sides of Hexadecagon, The Diagonal of Hexadecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of the Hexadecagon, calculated using the inradius. Diagonal across Three Sides of Hexadecagon is denoted by d₃ symbol.

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

FAQs on Diagonal of Hexadecagon across Three Sides given Inradius

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

The formula of Diagonal of Hexadecagon across Three Sides given Inradius is expressed as Diagonal across Three Sides of Hexadecagon = sin((3*pi)/16)/sin(pi/16)*(2*Inradius of Hexadecagon)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))). Here is an example- 13.59491 = sin((3*pi)/16)/sin(pi/16)*(2*12)/(1+sqrt(2)+sqrt(2*(2+sqrt(2)))).

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

With Inradius of Hexadecagon (r_i) we can find Diagonal of Hexadecagon across Three Sides given Inradius using the formula - Diagonal across Three Sides of Hexadecagon = sin((3*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 Three Sides of Hexadecagon?

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

Diagonal across Three Sides of Hexadecagon=sin((3*pi)/16)/sin(pi/16)*Side of Hexadecagon
Diagonal across Three Sides of Hexadecagon=Height of Hexadecagon*sin((3*pi)/16)/sin((7*pi)/16)
Diagonal across Three Sides of Hexadecagon=sqrt(Area of Hexadecagon/(4*cot(pi/16)))*sin((3*pi)/16)/sin(pi/16)

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

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

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

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

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