Edge Length of Pentagon given Height using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))
le = (h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
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., sin(Angle)
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
Edge Length of Pentagon - (Measured in Meter) - The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.
Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
STEP 1: Convert Input(s) to Base Unit
Height of Pentagon: 15 Meter --> 15 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
le = (h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))) --> (15*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))
Evaluating ... ...
le = 9.74759088698719
STEP 3: Convert Result to Output's Unit
9.74759088698719 Meter --> No Conversion Required
FINAL ANSWER
9.74759088698719 9.747591 Meter <-- Edge Length of Pentagon
(Calculation completed in 00.004 seconds)

Credits

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
Dhruv Walia has created this Calculator and 1100+ more calculators!
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Verified by Nikhil
Mumbai University (DJSCE), Mumbai
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16 Edge Length of Pentagon Calculators

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

Edge Length of Pentagon given Height using Interior Angle Formula

Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))
le = (h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(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 Edge Length of Pentagon given Height using Interior Angle?

Edge Length of Pentagon given Height using Interior Angle calculator uses Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))) to calculate the Edge Length of Pentagon, The Edge Length of Pentagon given Height using Interior Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using height and interior angle. Edge Length of Pentagon is denoted by le symbol.

How to calculate Edge Length of Pentagon given Height using Interior Angle using this online calculator? To use this online calculator for Edge Length of Pentagon given Height using Interior Angle, enter Height of Pentagon (h) and hit the calculate button. Here is how the Edge Length of Pentagon given Height using Interior Angle calculation can be explained with given input values -> 9.747591 = (15*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))).

FAQ

What is Edge Length of Pentagon given Height using Interior Angle?
The Edge Length of Pentagon given Height using Interior Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using height and interior angle and is represented as le = (h*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))) or Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))). Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
How to calculate Edge Length of Pentagon given Height using Interior Angle?
The Edge Length of Pentagon given Height using Interior Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using height and interior angle is calculated using Edge Length of Pentagon = (Height of Pentagon*sin(3/5*pi))/((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi))). To calculate Edge Length of Pentagon given Height using Interior Angle, you need Height of Pentagon (h). With our tool, you need to enter the respective value for Height 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 Edge Length of Pentagon?
In this formula, Edge Length of Pentagon uses Height of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -
  • Edge Length of Pentagon = (2*Area of Pentagon)/(5*Inradius of Pentagon)
  • Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))
  • Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))
  • Edge Length of Pentagon = sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))
  • Edge Length of Pentagon = Height of Pentagon*2/sqrt(5+(2*sqrt(5)))
  • Edge Length of Pentagon = Circumradius of Pentagon*10/sqrt(50+(10*sqrt(5)))
  • Edge Length of Pentagon = Width of Pentagon*2/(1+sqrt(5))
  • Edge Length of Pentagon = 2*Circumradius of Pentagon*sin(pi/5)
  • Edge Length of Pentagon = 2*Inradius of Pentagon*tan(pi/5)
  • Edge Length of Pentagon = sqrt((Area of Pentagon*4*tan(pi/5))/5)
  • Edge Length of Pentagon = Perimeter of Pentagon/5
  • Edge Length of Pentagon = Diagonal of Pentagon*2/(1+sqrt(5))
  • Edge Length of Pentagon = sqrt(((2*sin(3/5*pi))*Area of Pentagon)/(5*(1/2-cos(3/5*pi))^2))
  • Edge Length of Pentagon = Circumradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))
  • Edge Length of Pentagon = Inradius of Pentagon*sin(3/5*pi)/(1/2-cos(3/5*pi))^2
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