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Circumradius of Pentagon given Edge Length using Interior Angle Formula

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GoCircumradius of Pentagon given Edge Length using Central Angle Formula

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

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

r_c - Circumradius of Pentagon?l_e - Edge Length of Pentagon?π - Archimedes' constant?

Circumradius of Pentagon given Edge Length using Interior Angle Example

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

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

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

8.5065 = \frac{10 \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

8.5065m = \frac{10m \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

8.5065 = \frac{10 \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

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Circumradius of Pentagon given Edge Length using Interior Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r c = \frac{10m \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}{\sin (\frac{3}{5} \cdot π)}

Next Step Substitute values of Constants

∴

r c = \frac{10m \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

Next Step Prepare to Evaluate

∴

r c = \frac{10 \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}{\sin (\frac{3}{5} \cdot 3.1416)}

Next Step Evaluate

∴

r c = 8.5065080835204m

LAST Step Rounding Answer

∴

r c = 8.5065m

Circumradius of Pentagon given Edge Length using Interior Angle Formula Elements

Variables

Constants

Functions

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

Edge Length of Pentagon

The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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

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)

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 Circumradius of Pentagon

Go Circumradius of Pentagon

r c = \frac{l e}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

Go Circumradius of Pentagon given Edge Length using Central Angle

r c = \frac{l e}{2 \cdot \sin (\frac{π}{5})}

Go Circumradius of Pentagon given Height and Inradius

r c = h - r i

Other formulas in Circumradius of Pentagon category

Go Inradius of Pentagon

r i = \frac{l e}{10} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

Go Inradius of Pentagon given Area and Edge Length

r i = \frac{2 \cdot A}{5 \cdot l e}

Go Inradius of Pentagon given Circumradius and Height

r i = h - r c

Go Inradius of Pentagon given Edge Length using Central Angle

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

How to Evaluate Circumradius of Pentagon given Edge Length using Interior Angle?

Circumradius of Pentagon given Edge Length using Interior Angle evaluator uses Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi)) to evaluate the Circumradius of Pentagon, The Circumradius of Pentagon given Edge Length using Interior Angle is defined as the length of the line joining the center of the Pentagon to point on the circumcircle of the Pentagon, calculated using edge length and interior angle. Circumradius of Pentagon is denoted by r_c symbol.

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

FAQs on Circumradius of Pentagon given Edge Length using Interior Angle

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

The formula of Circumradius of Pentagon given Edge Length using Interior Angle is expressed as Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi)). Here is an example- 8.506508 = (10*(1/2-cos(3/5*pi)))/(sin(3/5*pi)).

How to calculate Circumradius of Pentagon given Edge Length using Interior Angle?

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

What are the other ways to Calculate Circumradius of Pentagon?

Here are the different ways to Calculate Circumradius of Pentagon-

Circumradius of Pentagon=Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))
Circumradius of Pentagon=(Edge Length of Pentagon)/(2*sin(pi/5))
Circumradius of Pentagon=Height of Pentagon-Inradius of Pentagon

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

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

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

Circumradius of Pentagon given Edge Length 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 Circumradius of Pentagon given Edge Length using Interior Angle can be measured.

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