## Height of Pentagon given Circumradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))
h = rc*(3/2-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
Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
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
h = rc*(3/2-cos(3/5*pi)) --> 9*(3/2-cos(3/5*pi))
Evaluating ... ...
h = 16.2811529493745
STEP 3: Convert Result to Output's Unit
16.2811529493745 Meter --> No Conversion Required
16.2811529493745 16.28115 Meter <-- Height of Pentagon
(Calculation completed in 00.004 seconds)
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## < 16 Height of Pentagon Calculators

Height of Pentagon given Area using Interior Angle
Height of Pentagon = sqrt((4*tan(pi/5)*Area of Pentagon)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
Height of Pentagon given Area using Central Angle
Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))
Height of Pentagon given Edge Length using Interior Angle
Height of Pentagon = Edge Length of Pentagon*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
Height of Pentagon given Area
Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon
Height of Pentagon given Edge Length using Central Angle
Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
Height of Pentagon given Diagonal
Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon given Width
Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
Height of Pentagon given Inradius using Interior Angle
Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
Height of Pentagon
Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
Height of Pentagon given Circumradius using Interior Angle
Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))
Height of Pentagon given Perimeter
Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
Height of Pentagon given Circumradius using Central Angle
Height of Pentagon = Circumradius of Pentagon*(1+cos(pi/5))
Height of Pentagon given Inradius using Central angle
Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5)))
Height of Pentagon = sqrt(5)*Inradius of Pentagon

## Height of Pentagon given Circumradius using Interior Angle Formula

Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi))
h = rc*(3/2-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 Height of Pentagon given Circumradius using Interior Angle?

Height of Pentagon given Circumradius using Interior Angle calculator uses Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi)) to calculate the Height of Pentagon, The Height of Pentagon given Circumradius using Interior Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its circumradius and interior angle. Height of Pentagon is denoted by h symbol.

How to calculate Height of Pentagon given Circumradius using Interior Angle using this online calculator? To use this online calculator for Height of Pentagon given Circumradius using Interior Angle, enter Circumradius of Pentagon (rc) and hit the calculate button. Here is how the Height of Pentagon given Circumradius using Interior Angle calculation can be explained with given input values -> 16.28115 = 9*(3/2-cos(3/5*pi)).

### FAQ

What is Height of Pentagon given Circumradius using Interior Angle?
The Height of Pentagon given Circumradius using Interior Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its circumradius and interior angle and is represented as h = rc*(3/2-cos(3/5*pi)) or Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi)). The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.
How to calculate Height of Pentagon given Circumradius using Interior Angle?
The Height of Pentagon given Circumradius using Interior Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its circumradius and interior angle is calculated using Height of Pentagon = Circumradius of Pentagon*(3/2-cos(3/5*pi)). To calculate Height of Pentagon given Circumradius using Interior Angle, you need Circumradius of Pentagon (rc). 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 Height of Pentagon?
In this formula, Height of Pentagon uses Circumradius of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -
• Height of Pentagon = Circumradius of Pentagon*(1+cos(pi/5))
• Height of Pentagon = Inradius of Pentagon*(1+(1/cos(pi/5)))
• Height of Pentagon = Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
• Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon
• Height of Pentagon = sqrt(5)*Inradius of Pentagon
• Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5)))
• Height of Pentagon = sqrt(5+(2*sqrt(5)))/2*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
• Height of Pentagon = Perimeter of Pentagon*sqrt(5+(2*sqrt(5)))/10
• Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
• Height of Pentagon = Diagonal of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5))
• Height of Pentagon = ((1+cos(pi/5))*sqrt((4*tan(pi/5)*Area of Pentagon)/5))/(2*sin(pi/5))
• Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
• Height of Pentagon = sqrt((4*tan(pi/5)*Area of Pentagon)/5)*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
• Height of Pentagon = Edge Length of Pentagon*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)
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