Height of Hexadecagon given Circumradius Calculator

✖Circumradius of Hexadecagon is the radius of a circumcircle touching each of the Hexadecagon's vertices.ⓘ Circumradius of Hexadecagon [r_c]

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✖Height of Hexadecagon is the length of a perpendicular line drawn from one vertex to the opposite side.ⓘ Height of Hexadecagon given Circumradius [h]

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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)*r_c/(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 - 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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., 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)*r_c/(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 ≈ 25.50042 Meter <-- Height of Hexadecagon

(Calculation completed in 00.004 seconds)

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< Height of Hexadecagon Calculators

Height of Hexadecagon given Diagonal across Five Sides

LaTeX Go Height of Hexadecagon = Diagonal across Five Sides of Hexadecagon*sin((7*pi)/16)/sin((5*pi)/16)

Height of Hexadecagon given Diagonal across Six Sides

LaTeX Go Height of Hexadecagon = Diagonal across Six Sides of Hexadecagon*sin((7*pi)/16)/sin((3*pi)/8)

Height of Hexadecagon

LaTeX Go Height of Hexadecagon = sin((7*pi)/16)/sin(pi/16)*Side of Hexadecagon

Height of Hexadecagon given Diagonal across Eight Sides

LaTeX Go Height of Hexadecagon = Diagonal across Eight Sides of Hexadecagon*sin((7*pi)/16)

Height of Hexadecagon given Circumradius Formula

LaTeX Go

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 (r_c) 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)*r_c/(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 (r_c). 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 3 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)

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