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Height of Nonagon given Diagonal across Three Sides Formula

GoHeight of Nonagon Formula

GoHeight of Nonagon given Area Formula

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Height of Nonagon is the length of a perpendicular line drawn from one vertex to the opposite side. Check FAQs

h = d 3 \cdot \frac{\sin (\frac{π}{9})}{2 \cdot \sin (3 \cdot \frac{π}{9}) \cdot \tan (\frac{π}{18})}

h - Height of Nonagon?d₃ - Diagonal across Three Sides of Nonagon?π - Archimedes' constant?

Height of Nonagon given Diagonal across Three Sides Example

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

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

Here is how the Height of Nonagon given Diagonal across Three Sides equation looks like.

22.3976 = 20 \cdot \frac{\sin (\frac{3.1416}{9})}{2 \cdot \sin (3 \cdot \frac{3.1416}{9}) \cdot \tan (\frac{3.1416}{18})}

22.3976m = 20m \cdot \frac{\sin (\frac{3.1416}{9})}{2 \cdot \sin (3 \cdot \frac{3.1416}{9}) \cdot \tan (\frac{3.1416}{18})}

22.3976 = 20 \cdot \frac{\sin (\frac{3.1416}{9})}{2 \cdot \sin (3 \cdot \frac{3.1416}{9}) \cdot \tan (\frac{3.1416}{18})}

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Height of Nonagon given Diagonal across Three Sides Solution

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

FIRST Step Consider the formula

h = d 3 \cdot \frac{\sin (\frac{π}{9})}{2 \cdot \sin (3 \cdot \frac{π}{9}) \cdot \tan (\frac{π}{18})}

Next Step Substitute values of Variables

∴

h = 20m \cdot \frac{\sin (\frac{π}{9})}{2 \cdot \sin (3 \cdot \frac{π}{9}) \cdot \tan (\frac{π}{18})}

Next Step Substitute values of Constants

∴

h = 20m \cdot \frac{\sin (\frac{3.1416}{9})}{2 \cdot \sin (3 \cdot \frac{3.1416}{9}) \cdot \tan (\frac{3.1416}{18})}

Next Step Prepare to Evaluate

∴

h = 20 \cdot \frac{\sin (\frac{3.1416}{9})}{2 \cdot \sin (3 \cdot \frac{3.1416}{9}) \cdot \tan (\frac{3.1416}{18})}

Next Step Evaluate

∴

h = 22.3976411351175m

LAST Step Rounding Answer

∴

h = 22.3976m

Height of Nonagon given Diagonal across Three Sides Formula Elements

Variables

Constants

Functions

Height of Nonagon

Height of Nonagon is the length of a perpendicular line drawn from one vertex to the opposite side.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Nonagon

Diagonal across Three Sides of Nonagon

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

Symbol: d₃

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal across Three Sides of Nonagon

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 Height of Nonagon

Go Height of Nonagon

h = r c + r i

Go Height of Nonagon given Area

h = (\frac{1 + \cos (\frac{π}{9})}{3 \cdot \sin (\frac{π}{9})}) \cdot \sqrt{A \cdot (\tan (\frac{π}{9}))}

Go Height of Nonagon given Inradius

h = r i \cdot (1 + \sec (\frac{π}{9}))

Go Height of Nonagon given Side

h = (\frac{1 + \cos (\frac{π}{9})}{2 \cdot \sin (\frac{π}{9})}) \cdot S

How to Evaluate Height of Nonagon given Diagonal across Three Sides?

Height of Nonagon given Diagonal across Three Sides evaluator uses Height of Nonagon = Diagonal across Three Sides of Nonagon*sin(pi/9)/(2*sin(3*pi/9)*tan(pi/18)) to evaluate the Height of Nonagon, The Height of Nonagon given Diagonal across Three Sides formula is defined as the perpendicular distance between the apex of the Nonagon and a point on its opposite side using the diagonal across three sides. Height of Nonagon is denoted by h symbol.

How to evaluate Height of Nonagon given Diagonal across Three Sides using this online evaluator? To use this online evaluator for Height of Nonagon given Diagonal across Three Sides, enter Diagonal across Three Sides of Nonagon (d₃) and hit the calculate button.

FAQs on Height of Nonagon given Diagonal across Three Sides

What is the formula to find Height of Nonagon given Diagonal across Three Sides?

The formula of Height of Nonagon given Diagonal across Three Sides is expressed as Height of Nonagon = Diagonal across Three Sides of Nonagon*sin(pi/9)/(2*sin(3*pi/9)*tan(pi/18)). Here is an example- 22.39764 = 20*sin(pi/9)/(2*sin(3*pi/9)*tan(pi/18)).

How to calculate Height of Nonagon given Diagonal across Three Sides?

With Diagonal across Three Sides of Nonagon (d₃) we can find Height of Nonagon given Diagonal across Three Sides using the formula - Height of Nonagon = Diagonal across Three Sides of Nonagon*sin(pi/9)/(2*sin(3*pi/9)*tan(pi/18)). This formula also uses Archimedes' constant and , Sine (sin), Tangent (tan) function(s).

What are the other ways to Calculate Height of Nonagon?

Here are the different ways to Calculate Height of Nonagon-

Height of Nonagon=Circumradius of Nonagon+Inradius of Nonagon
Height of Nonagon=((1+cos(pi/9))/(3*sin(pi/9)))*sqrt(Area of Nonagon*(tan(pi/9)))
Height of Nonagon=Inradius of Nonagon*(1+sec(pi/9))

Can the Height of Nonagon given Diagonal across Three Sides be negative?

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

Which unit is used to measure Height of Nonagon given Diagonal across Three Sides?

Height of Nonagon given Diagonal across Three Sides is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Nonagon given Diagonal across Three Sides can be measured.

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