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Inradius of Pentagon given Circumradius using Interior Angle Formula

GoInradius of Pentagon given Edge Length using Central Angle Formula

GoInradius of Pentagon given Circumradius using Central Angle Formula

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

r i = r c \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))

r_i - Inradius of Pentagon?r_c - Circumradius of Pentagon?π - Archimedes' constant?

Inradius of Pentagon given Circumradius using Interior Angle Example

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Here is how the Inradius of Pentagon given Circumradius using Interior Angle equation looks like with Values.

Here is how the Inradius of Pentagon given Circumradius using Interior Angle equation looks like with Units.

Here is how the Inradius of Pentagon given Circumradius using Interior Angle equation looks like.

7.2812 = 9 \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))

7.2812m = 9m \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))

7.2812 = 9 \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))

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Inradius of Pentagon given Circumradius using Interior Angle Solution

Follow our step by step solution on how to calculate Inradius of Pentagon given Circumradius using Interior Angle?

FIRST Step Consider the formula

r i = r c \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))

Next Step Substitute values of Variables

∴

r i = 9m \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))

Next Step Substitute values of Constants

∴

r i = 9m \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))

Next Step Prepare to Evaluate

∴

r i = 9 \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))

Next Step Evaluate

∴

r i = 7.28115294937453m

LAST Step Rounding Answer

∴

r i = 7.2812m

Inradius of Pentagon given Circumradius using Interior Angle Formula Elements

Variables

Constants

Functions

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

Circumradius of Pentagon

The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius 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 Inradius of Pentagon

Go Inradius of Pentagon given Edge Length using Central Angle

r i = \frac{l e}{2 \cdot \tan (\frac{π}{5})}

Go Inradius of Pentagon given Circumradius using Central Angle

r i = r c \cdot \cos (\frac{π}{5})

Go Inradius of Pentagon given Circumradius

r i = \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}} \cdot r c

Go Inradius of Pentagon given Height using Central Angle

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

How to Evaluate Inradius of Pentagon given Circumradius using Interior Angle?

Inradius of Pentagon given Circumradius using Interior Angle evaluator uses Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)) to evaluate the Inradius of Pentagon, The Inradius of Pentagon given Circumradius using Interior Angle is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using circumradius and interior angle. Inradius of Pentagon is denoted by r_i symbol.

How to evaluate Inradius of Pentagon given Circumradius using Interior Angle using this online evaluator? To use this online evaluator for Inradius of Pentagon given Circumradius using Interior Angle, enter Circumradius of Pentagon (r_c) and hit the calculate button.

FAQs on Inradius of Pentagon given Circumradius using Interior Angle

What is the formula to find Inradius of Pentagon given Circumradius using Interior Angle?

The formula of Inradius of Pentagon given Circumradius using Interior Angle is expressed as Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)). Here is an example- 7.281153 = 9*(1/2-cos(3/5*pi)).

How to calculate Inradius of Pentagon given Circumradius using Interior Angle?

With Circumradius of Pentagon (r_c) we can find Inradius of Pentagon given Circumradius using Interior Angle using the formula - Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)). This formula also uses Archimedes' constant and Cosine (cos) function(s).

What are the other ways to Calculate Inradius of Pentagon?

Here are the different ways to Calculate Inradius of Pentagon-

Inradius of Pentagon=(Edge Length of Pentagon)/(2*tan(pi/5))
Inradius of Pentagon=Circumradius of Pentagon*cos(pi/5)
Inradius of Pentagon=sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))*Circumradius of Pentagon

Can the Inradius of Pentagon given Circumradius using Interior Angle be negative?

No, the Inradius of Pentagon given Circumradius using Interior Angle, measured in Length cannot be negative.

Which unit is used to measure Inradius of Pentagon given Circumradius using Interior Angle?

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

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