Inradius of Pentagon given Circumradius using Interior Angle Calculator

✖The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.ⓘ Circumradius of Pentagon [r_c]

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✖The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.ⓘ Inradius of Pentagon given Circumradius using Interior Angle [r_i]

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Inradius of Pentagon given Circumradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi))
r_i = r_c*(1/2-cos(3/5*pi))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.
Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Pentagon: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = r_c*(1/2-cos(3/5*pi)) --> 9*(1/2-cos(3/5*pi))

Evaluating ... ...

r_i = 7.28115294937453

STEP 3: Convert Result to Output's Unit

7.28115294937453 Meter --> No Conversion Required

FINAL ANSWER

7.28115294937453 ≈ 7.281153 Meter <-- Inradius of Pentagon

(Calculation completed in 00.004 seconds)

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< Inradius of Pentagon Calculators

Inradius of Pentagon given Circumradius

LaTeX Go Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))*Circumradius of Pentagon

Inradius of Pentagon given Edge Length using Central Angle

LaTeX Go Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))

Inradius of Pentagon given Height using Central Angle

LaTeX Go Inradius of Pentagon = (Height of Pentagon)/(1+(1/cos(pi/5)))

Inradius of Pentagon given Circumradius using Central Angle

LaTeX Go Inradius of Pentagon = Circumradius of Pentagon*cos(pi/5)

Inradius of Pentagon given Circumradius using Interior Angle Formula

LaTeX Go

Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi))
r_i = r_c*(1/2-cos(3/5*pi))

What is Pentagon?

A Pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape. In geometry, it is considered as a five-sided polygon with five straight sides and five interior angles, which add up to 540°. Pentagons can be simple or self-intersecting. A simple pentagon (5-gon) must have five straight sides that meet to create five vertices but do not intersect with each other. A self-intersecting regular pentagon is called a pentagram.

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

Inradius of Pentagon given Circumradius using Interior Angle calculator uses Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)) to calculate 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 calculate Inradius of Pentagon given Circumradius using Interior Angle using this online calculator? To use this online calculator for Inradius of Pentagon given Circumradius using Interior Angle, enter Circumradius of Pentagon (r_c) and hit the calculate button. Here is how the Inradius of Pentagon given Circumradius using Interior Angle calculation can be explained with given input values -> 7.281153 = 9*(1/2-cos(3/5*pi)).

FAQ

What is Inradius of Pentagon given Circumradius using Interior Angle?

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 and is represented as r_i = r_c*(1/2-cos(3/5*pi)) or Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)). The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

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

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 is calculated using Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)). To calculate Inradius of Pentagon given Circumradius using Interior Angle, you need Circumradius of Pentagon (r_c). With our tool, you need to enter the respective value for Circumradius of Pentagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Inradius of Pentagon?

In this formula, Inradius of Pentagon uses Circumradius of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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