Height of Hexadecagon given Circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Circumradius of Hexadecagon/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))
h = (sin(7*pi/16)/sin(pi/16))*rc/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Height of Hexadecagon - (Measured in Meter) - Height of Hexadecagon is the length of a perpendicular line drawn from one vertex to the opposite side.
Circumradius of Hexadecagon - (Measured in Meter) - Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
STEP 1: Convert Input(s) to Base Unit
Circumradius of Hexadecagon: 13 Meter --> 13 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = (sin(7*pi/16)/sin(pi/16))*rc/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))) --> (sin(7*pi/16)/sin(pi/16))*13/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))
Evaluating ... ...
h = 25.500417290484
STEP 3: Convert Result to Output's Unit
25.500417290484 Meter --> No Conversion Required
FINAL ANSWER
25.500417290484 Meter <-- Height of Hexadecagon
(Calculation completed in 00.011 seconds)

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10+ Height of Hexadecagon Calculators

Height of Hexadecagon given Circumradius
Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Circumradius of Hexadecagon/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))) Go
Height of Hexadecagon given Diagonal across Three Sides
Height of Hexadecagon = Diagonal across Three Sides of Hexadecagon*(sin(7*pi/16)/sin(3*pi/16)) Go
Height of Hexadecagon given Diagonal across Five Sides
Height of Hexadecagon = Diagonal across Five Sides of Hexadecagon*(sin(7*pi/16)/sin(5*pi/16)) Go
Height of Hexadecagon given Diagonal across Six Sides
Height of Hexadecagon = Diagonal across Six Sides of Hexadecagon*(sin(7*pi/16)/sin(3*pi/8)) Go
Height of Hexadecagon given Diagonal across Two Sides
Height of Hexadecagon = Diagonal across Two Sides of Hexadecagon*(sin(7*pi/16)/sin(pi/8)) Go
Height of Hexadecagon given Perimeter
Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*(Perimeter of Hexadecagon/16) Go
Height of Hexadecagon
Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Side of Hexadecagon Go
Height of Hexadecagon given Area
Height of Hexadecagon = sqrt(Area of Hexadecagon/(4*tan(pi/16))) Go
Height of Hexadecagon given Diagonal across Eight Sides
Height of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin(7*pi/16) Go
Height of Hexadecagon given Inradius
Height of Hexadecagon = 2*Inradius of Hexadecagon Go

Height of Hexadecagon given Circumradius Formula

Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Circumradius of Hexadecagon/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))
h = (sin(7*pi/16)/sin(pi/16))*rc/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2)))

What is Hexadecagon?

A Hexadecagon is a 16-sided polygon, in which all angles are equal and all sides are congruent. Each angle of a regular hexadecagon is 157.5 degrees, and the total angle measure of any hexadecagon is 2520 degrees. Hexadecagons are sometimes used in art and architecture.

How to Calculate Height of Hexadecagon given Circumradius?

Height of Hexadecagon given Circumradius calculator uses Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Circumradius of Hexadecagon/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))) to calculate the Height of Hexadecagon, The Height of Hexadecagon given Circumradius formula is defined as the length of the perpendicular line drawn from one vertex to the opposite side of Hexadecagon, calculated using circumradius. Height of Hexadecagon is denoted by h symbol.

How to calculate Height of Hexadecagon given Circumradius using this online calculator? To use this online calculator for Height of Hexadecagon given Circumradius, enter Circumradius of Hexadecagon (rc) and hit the calculate button. Here is how the Height of Hexadecagon given Circumradius calculation can be explained with given input values -> 25.50042 = (sin(7*pi/16)/sin(pi/16))*13/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))).

FAQ

What is Height of Hexadecagon given Circumradius?
The Height of Hexadecagon given Circumradius formula is defined as the length of the perpendicular line drawn from one vertex to the opposite side of Hexadecagon, calculated using circumradius and is represented as h = (sin(7*pi/16)/sin(pi/16))*rc/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))) or Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Circumradius of Hexadecagon/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))). Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.
How to calculate Height of Hexadecagon given Circumradius?
The Height of Hexadecagon given Circumradius formula is defined as the length of the perpendicular line drawn from one vertex to the opposite side of Hexadecagon, calculated using circumradius is calculated using Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Circumradius of Hexadecagon/((sqrt((4+(2*sqrt(2))+sqrt(20+(14*sqrt(2))))/2))). To calculate Height of Hexadecagon given Circumradius, you need Circumradius of Hexadecagon (rc). With our tool, you need to enter the respective value for Circumradius of Hexadecagon 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 Hexadecagon?
In this formula, Height of Hexadecagon uses Circumradius of Hexadecagon. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*Side of Hexadecagon
  • Height of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin(7*pi/16)
  • Height of Hexadecagon = Diagonal across Six Sides of Hexadecagon*(sin(7*pi/16)/sin(3*pi/8))
  • Height of Hexadecagon = Diagonal across Five Sides of Hexadecagon*(sin(7*pi/16)/sin(5*pi/16))
  • Height of Hexadecagon = Diagonal across Three Sides of Hexadecagon*(sin(7*pi/16)/sin(3*pi/16))
  • Height of Hexadecagon = Diagonal across Two Sides of Hexadecagon*(sin(7*pi/16)/sin(pi/8))
  • Height of Hexadecagon = sqrt(Area of Hexadecagon/(4*tan(pi/16)))
  • Height of Hexadecagon = (sin(7*pi/16)/sin(pi/16))*(Perimeter of Hexadecagon/16)
  • Height of Hexadecagon = 2*Inradius of Hexadecagon
  • Height of Hexadecagon = Diagonal across Four Sides of Hexadecagon*(sin(7*pi/16)/sin(4*pi/16))
  • Height of Hexadecagon = Diagonal across Seven Sides of Hexadecagon/1
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