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Height of Pentagon given Inradius using Central angle Formula

GoHeight of Pentagon given Circumradius and Inradius Formula

GoHeight of Pentagon given Circumradius using Central Angle Formula

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Height of Pentagon is the distance between one side of Pentagon and its opposite vertex. Check FAQs

h = r i \cdot (1 + (\frac{1}{\cos (\frac{π}{5})}))

h - Height of Pentagon?r_i - Inradius of Pentagon?π - Archimedes' constant?

Height of Pentagon given Inradius using Central angle Example

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Here is how the Height of Pentagon given Inradius using Central angle equation looks like with Values.

Here is how the Height of Pentagon given Inradius using Central angle equation looks like with Units.

Here is how the Height of Pentagon given Inradius using Central angle equation looks like.

15.6525 = 7 \cdot (1 + (\frac{1}{\cos (\frac{3.1416}{5})}))

15.6525m = 7m \cdot (1 + (\frac{1}{\cos (\frac{3.1416}{5})}))

15.6525 = 7 \cdot (1 + (\frac{1}{\cos (\frac{3.1416}{5})}))

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Height of Pentagon given Inradius using Central angle Solution

Follow our step by step solution on how to calculate Height of Pentagon given Inradius using Central angle?

FIRST Step Consider the formula

h = r i \cdot (1 + (\frac{1}{\cos (\frac{π}{5})}))

Next Step Substitute values of Variables

∴

h = 7m \cdot (1 + (\frac{1}{\cos (\frac{π}{5})}))

Next Step Substitute values of Constants

∴

h = 7m \cdot (1 + (\frac{1}{\cos (\frac{3.1416}{5})}))

Next Step Prepare to Evaluate

∴

h = 7 \cdot (1 + (\frac{1}{\cos (\frac{3.1416}{5})}))

Next Step Evaluate

∴

h = 15.6524758424985m

LAST Step Rounding Answer

∴

h = 15.6525m

Height of Pentagon given Inradius using Central angle Formula Elements

Variables

Constants

Functions

Height of Pentagon

Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Pentagon

Inradius of Pentagon

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Height of Pentagon

Go Height of Pentagon given Circumradius and Inradius

h = r c + r i

Go Height of Pentagon given Circumradius using Central Angle

h = r c \cdot (1 + \cos (\frac{π}{5}))

Go Height of Pentagon given Edge Length using Central Angle

h = \frac{l e}{2} \cdot \frac{1 + \cos (\frac{π}{5})}{\sin (\frac{π}{5})}

Go Height of Pentagon given Circumradius

h = 5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}) \cdot r c

How to Evaluate Height of Pentagon given Inradius using Central angle?

Height of Pentagon given Inradius using Central angle evaluator uses Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5))) to evaluate the Height of Pentagon, Height of Pentagon given Inradius using Central angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its inradius and central angle. Height of Pentagon is denoted by h symbol.

How to evaluate Height of Pentagon given Inradius using Central angle using this online evaluator? To use this online evaluator for Height of Pentagon given Inradius using Central angle, enter Inradius of Pentagon (r_i) and hit the calculate button.

FAQs on Height of Pentagon given Inradius using Central angle

What is the formula to find Height of Pentagon given Inradius using Central angle?

The formula of Height of Pentagon given Inradius using Central angle is expressed as Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5))). Here is an example- 15.65248 = 7*(1+(1/cos(pi/5))).

How to calculate Height of Pentagon given Inradius using Central angle?

With Inradius of Pentagon (r_i) we can find Height of Pentagon given Inradius using Central angle using the formula - Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5))). This formula also uses Archimedes' constant and Cosine function(s).

What are the other ways to Calculate Height of Pentagon?

Here are the different ways to Calculate Height of Pentagon-

Height of Pentagon=Circumradius of Pentagon+Inradius of Pentagon
Height of Pentagon=Circumradius of Pentagon*(1+cos(pi/5))
Height of Pentagon=Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)

Can the Height of Pentagon given Inradius using Central angle be negative?

No, the Height of Pentagon given Inradius using Central angle, measured in Length cannot be negative.

Which unit is used to measure Height of Pentagon given Inradius using Central angle?

Height of Pentagon given Inradius using Central angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Pentagon given Inradius using Central angle can be measured.

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