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Diagonal of Hendecagon across Three Sides given Inradius Formula

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

d 3 = 2 \cdot \tan (\frac{π}{11}) \cdot r i \cdot \frac{\sin (\frac{3 \cdot π}{11})}{\sin (\frac{π}{11})}

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

Diagonal of Hendecagon across Three Sides given Inradius Example

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

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

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

12.6025 = 2 \cdot \tan (\frac{3.1416}{11}) \cdot 8 \cdot \frac{\sin (\frac{3 \cdot 3.1416}{11})}{\sin (\frac{3.1416}{11})}

12.6025m = 2 \cdot \tan (\frac{3.1416}{11}) \cdot 8m \cdot \frac{\sin (\frac{3 \cdot 3.1416}{11})}{\sin (\frac{3.1416}{11})}

12.6025 = 2 \cdot \tan (\frac{3.1416}{11}) \cdot 8 \cdot \frac{\sin (\frac{3 \cdot 3.1416}{11})}{\sin (\frac{3.1416}{11})}

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Diagonal of Hendecagon across Three Sides given Inradius Solution

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

FIRST Step Consider the formula

d 3 = 2 \cdot \tan (\frac{π}{11}) \cdot r i \cdot \frac{\sin (\frac{3 \cdot π}{11})}{\sin (\frac{π}{11})}

Next Step Substitute values of Variables

∴

d 3 = 2 \cdot \tan (\frac{π}{11}) \cdot 8m \cdot \frac{\sin (\frac{3 \cdot π}{11})}{\sin (\frac{π}{11})}

Next Step Substitute values of Constants

∴

d 3 = 2 \cdot \tan (\frac{3.1416}{11}) \cdot 8m \cdot \frac{\sin (\frac{3 \cdot 3.1416}{11})}{\sin (\frac{3.1416}{11})}

Next Step Prepare to Evaluate

∴

d 3 = 2 \cdot \tan (\frac{3.1416}{11}) \cdot 8 \cdot \frac{\sin (\frac{3 \cdot 3.1416}{11})}{\sin (\frac{3.1416}{11})}

Next Step Evaluate

∴

d 3 = 12.6024822715653m

LAST Step Rounding Answer

∴

d 3 = 12.6025m

Diagonal of Hendecagon across Three Sides given Inradius Formula Elements

Variables

Constants

Functions

Diagonal across Three Sides of Hendecagon

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

Symbol: d₃

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Three Sides of Hendecagon

Inradius of Hendecagon

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Hendecagon

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)

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other Formulas to find Diagonal across Three Sides of Hendecagon

Go Diagonal of Hendecagon across Three Sides

d 3 = \frac{S \cdot \sin (\frac{3 \cdot π}{11})}{\sin (\frac{π}{11})}

Go Diagonal of Hendecagon across Three Sides given Area

d 3 = \sqrt{\frac{4 \cdot A \cdot \tan (\frac{π}{11})}{11}} \cdot \frac{\sin (\frac{3 \cdot π}{11})}{\sin (\frac{π}{11})}

Go Diagonal of Hendecagon across Three Sides given Height

d 3 = 2 \cdot \tan (\frac{π}{22}) \cdot h \cdot \frac{\sin (\frac{3 \cdot π}{11})}{\sin (\frac{π}{11})}

Go Diagonal of Hendecagon across Three Sides given Perimeter

d 3 = \frac{P}{11} \cdot \frac{\sin (\frac{3 \cdot π}{11})}{\sin (\frac{π}{11})}

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

Diagonal of Hendecagon across Three Sides given Inradius evaluator uses Diagonal across Three Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((3*pi)/11)/sin(pi/11) to evaluate the Diagonal across Three Sides of Hendecagon, The Diagonal of Hendecagon across Three Sides given Inradius formula is defined as the straight line connecting two non-adjacent vertices across three sides of Hendecagon, calculated using inradius. Diagonal across Three Sides of Hendecagon is denoted by d₃ symbol.

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

FAQs on Diagonal of Hendecagon across Three Sides given Inradius

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

The formula of Diagonal of Hendecagon across Three Sides given Inradius is expressed as Diagonal across Three Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((3*pi)/11)/sin(pi/11). Here is an example- 12.60248 = 2*tan(pi/11)*8*sin((3*pi)/11)/sin(pi/11).

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

With Inradius of Hendecagon (r_i) we can find Diagonal of Hendecagon across Three Sides given Inradius using the formula - Diagonal across Three Sides of Hendecagon = 2*tan(pi/11)*Inradius of Hendecagon*sin((3*pi)/11)/sin(pi/11). This formula also uses Archimedes' constant and , Sine (sin), Tangent (tan) function(s).

What are the other ways to Calculate Diagonal across Three Sides of Hendecagon?

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

Diagonal across Three Sides of Hendecagon=(Side of Hendecagon*sin((3*pi)/11))/sin(pi/11)
Diagonal across Three Sides of Hendecagon=sqrt((4*Area of Hendecagon*tan(pi/11))/11)*sin((3*pi)/11)/sin(pi/11)
Diagonal across Three Sides of Hendecagon=2*tan(pi/22)*Height of Hendecagon*sin((3*pi)/11)/sin(pi/11)

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

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

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

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

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