Outer Angle of Polygram given Chord Length Calculator

✖The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end.ⓘ Edge Length of Polygram [l_e]			+10% -10%
✖The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip.ⓘ Chord Length of Polygram [l_c]			+10% -10%

✖The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.ⓘ Outer Angle of Polygram given Chord Length [∠_Outer]

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Formula

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Outer Angle of Polygram given Chord Length

Formula

`"∠"_{"Outer"} = arccos(((2*"l"_{"e"}^2)-"l"_{"c"}^2)/(2*"l"_{"e"}^2))`

Example

`"106.2602°"=arccos(((2*("5m")^2)-("8m")^2)/(2*("5m")^2))`

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Outer Angle of Polygram given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2))
∠_Outer = arccos(((2*l_e^2)-l_c^2)/(2*l_e^2))
This formula uses 2 Functions, 3 Variables

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)
arccos - Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., arccos(Number)

Variables Used

Outer Angle of Polygram - (Measured in Radian) - The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.
Edge Length of Polygram - (Measured in Meter) - The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end.
Chord Length of Polygram - (Measured in Meter) - The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Polygram: 5 Meter --> 5 Meter No Conversion Required
Chord Length of Polygram: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Outer = arccos(((2*l_e^2)-l_c^2)/(2*l_e^2)) --> arccos(((2*5^2)-8^2)/(2*5^2))

Evaluating ... ...

∠_Outer = 1.85459043600322

STEP 3: Convert Result to Output's Unit

1.85459043600322 Radian -->106.260204708332 Degree (Check conversion here)

FINAL ANSWER

106.260204708332 ≈ 106.2602 Degree <-- Outer Angle of Polygram

(Calculation completed in 00.020 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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< 2 Outer Angle of Polygram Calculators

Outer Angle of Polygram given Chord Length

Go Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2))

Outer Angle of Polygram

Go Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram

Outer Angle of Polygram given Chord Length Formula

Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2))
∠_Outer = arccos(((2*l_e^2)-l_c^2)/(2*l_e^2))

What is Polygram ?

→ A Polygram is a regular n-sided polygon with identical isosceles triangles (also known as SPIKES) attached to each edge. → It looks like a n-pointed star. → For a n-pointed star, there will be n-spikes. → The Spike (Isosceles Triangle) is an important part of the polygram and it is defined using 4 parameters. They are : 1) The Base Length of the Triangle (a.k.a Base Length of the Polygram) 2) Length of the equal side of the triangle (a.k.a Edge Length of the Polygram) 3) Angle between the two equal sides of the isosceles triangle (a.k.a Inner Angle angle of the Polygram) 4) Height of the triangle (a.k.a Spike Height) Apart from these there are other important parameters that define the Polygram. They are: 1) Outer Angle : The angle between two adjacent isosceles triangles. 2) Chord Length : The distance between two peaks of the adjacent Spikes of the Polygram. 3) Perimeter : The sum of lengths of all the edges of the polygram. 4) Area : The amount of space occupied by the polygram.

How to Calculate Outer Angle of Polygram given Chord Length?

Outer Angle of Polygram given Chord Length calculator uses Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2)) to calculate the Outer Angle of Polygram, The Outer Angle of Polygram given Chord Length formula is defined as the angle between two adjacent isosceles triangles attached to the n-sided polygon of the whole Polygram and calculated using its chord length. Outer Angle of Polygram is denoted by ∠_Outer symbol.

How to calculate Outer Angle of Polygram given Chord Length using this online calculator? To use this online calculator for Outer Angle of Polygram given Chord Length, enter Edge Length of Polygram (l_e) & Chord Length of Polygram (l_c) and hit the calculate button. Here is how the Outer Angle of Polygram given Chord Length calculation can be explained with given input values -> 6088.261 = arccos(((2*5^2)-8^2)/(2*5^2)).

FAQ

What is Outer Angle of Polygram given Chord Length?

The Outer Angle of Polygram given Chord Length formula is defined as the angle between two adjacent isosceles triangles attached to the n-sided polygon of the whole Polygram and calculated using its chord length and is represented as ∠_Outer = arccos(((2*l_e^2)-l_c^2)/(2*l_e^2)) or Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2)). The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end & The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip.

How to calculate Outer Angle of Polygram given Chord Length?

The Outer Angle of Polygram given Chord Length formula is defined as the angle between two adjacent isosceles triangles attached to the n-sided polygon of the whole Polygram and calculated using its chord length is calculated using Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2)). To calculate Outer Angle of Polygram given Chord Length, you need Edge Length of Polygram (l_e) & Chord Length of Polygram (l_c). With our tool, you need to enter the respective value for Edge Length of Polygram & Chord Length of Polygram 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 Outer Angle of Polygram?

In this formula, Outer Angle of Polygram uses Edge Length of Polygram & Chord Length of Polygram. We can use 1 other way(s) to calculate the same, which is/are as follows -

Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram

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