Height of Pentagon given Inradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
h = ri*(1+(1/(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
Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.
STEP 1: Convert Input(s) to Base Unit
Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = ri*(1+(1/(1/2-cos(3/5*pi)))) --> 7*(1+(1/(1/2-cos(3/5*pi))))
Evaluating ... ...
h = 15.6524758424985
STEP 3: Convert Result to Output's Unit
15.6524758424985 Meter --> No Conversion Required
FINAL ANSWER
15.6524758424985 15.65248 Meter <-- Height of Pentagon
(Calculation completed in 00.004 seconds)

Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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16 Height of Pentagon Calculators

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

Height of Pentagon given Inradius using Interior Angle Formula

Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi))))
h = ri*(1+(1/(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 Height of Pentagon given Inradius using Interior Angle?

Height of Pentagon given Inradius using Interior Angle calculator uses Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi)))) to calculate the Height of Pentagon, The Height of Pentagon given Inradius using Interior Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its inradius and interior angle. Height of Pentagon is denoted by h symbol.

How to calculate Height of Pentagon given Inradius using Interior Angle using this online calculator? To use this online calculator for Height of Pentagon given Inradius using Interior Angle, enter Inradius of Pentagon (ri) and hit the calculate button. Here is how the Height of Pentagon given Inradius using Interior Angle calculation can be explained with given input values -> 15.65248 = 7*(1+(1/(1/2-cos(3/5*pi)))).

FAQ

What is Height of Pentagon given Inradius using Interior Angle?
The Height of Pentagon given Inradius using Interior Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its inradius and interior angle and is represented as h = ri*(1+(1/(1/2-cos(3/5*pi)))) or Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi)))). The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.
How to calculate Height of Pentagon given Inradius using Interior Angle?
The Height of Pentagon given Inradius using Interior Angle is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using its inradius and interior angle is calculated using Height of Pentagon = Inradius of Pentagon*(1+(1/(1/2-cos(3/5*pi)))). To calculate Height of Pentagon given Inradius using Interior Angle, you need Inradius of Pentagon (ri). With our tool, you need to enter the respective value for Inradius 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 Inradius of Pentagon. We can use 15 other way(s) to calculate the same, which is/are as follows -
  • Height of Pentagon = Circumradius of Pentagon+Inradius of Pentagon
  • 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 = Circumradius of Pentagon*(3/2-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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