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Outer Angle of Polygram given Chord Length Formula

GoOuter Angle of Polygram Formula

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The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram. Check FAQs

∠ Outer = \arccos (\frac{(2 \cdot {l e}^{2}) - {l c}^{2}}{2 \cdot {l e}^{2}})

∠_Outer - Outer Angle of Polygram?l_e - Edge Length of Polygram?l_c - Chord Length of Polygram?

Outer Angle of Polygram given Chord Length Example

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Here is how the Outer Angle of Polygram given Chord Length equation looks like with Values.

Here is how the Outer Angle of Polygram given Chord Length equation looks like with Units.

Here is how the Outer Angle of Polygram given Chord Length equation looks like.

106.2602 = \arccos (\frac{(2 \cdot 5^{2}) - 8^{2}}{2 \cdot 5^{2}})

106.2602° = \arccos (\frac{(2 \cdot {5m}^{2}) - {8m}^{2}}{2 \cdot {5m}^{2}})

106.2602 = \arccos (\frac{(2 \cdot 5^{2}) - 8^{2}}{2 \cdot 5^{2}})

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Outer Angle of Polygram given Chord Length Solution

Follow our step by step solution on how to calculate Outer Angle of Polygram given Chord Length?

FIRST Step Consider the formula

∠ Outer = \arccos (\frac{(2 \cdot {l e}^{2}) - {l c}^{2}}{2 \cdot {l e}^{2}})

Next Step Substitute values of Variables

∴

∠ Outer = \arccos (\frac{(2 \cdot {5m}^{2}) - {8m}^{2}}{2 \cdot {5m}^{2}})

Next Step Prepare to Evaluate

∴

∠ Outer = \arccos (\frac{(2 \cdot 5^{2}) - 8^{2}}{2 \cdot 5^{2}})

Next Step Evaluate

∴

∠ Outer = 1.85459043600322rad

Next Step Convert to Output's Unit

∴

∠ Outer = 106.260204708332°

LAST Step Rounding Answer

∴

∠ Outer = 106.2602°

Outer Angle of Polygram given Chord Length Formula Elements

Variables

Functions

Outer Angle of Polygram

The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.

Symbol: ∠_Outer

Measurement: AngleUnit: °

Note: Value should be between 0 to 300.

Formulas to find Outer Angle of Polygram

Edge Length of Polygram

The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Polygram

Chord Length of Polygram

The Chord Length of Polygram is the distance between any two adjacent spike tips of the Polygram from one tip to other tip.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Polygram

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: arccos(Number)

Other Formulas to find Outer Angle of Polygram

Go Outer Angle of Polygram

∠ Outer = \frac{2 \cdot π}{N Spikes} + ∠ Inner

How to Evaluate Outer Angle of Polygram given Chord Length?

Outer Angle of Polygram given Chord Length evaluator uses Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2)) to evaluate 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 evaluate Outer Angle of Polygram given Chord Length using this online evaluator? To use this online evaluator 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.

FAQs on Outer Angle of Polygram given Chord Length

What is the formula to find Outer Angle of Polygram given Chord Length?

The formula of Outer Angle of Polygram given Chord Length is expressed as Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2)). Here is an example- 6088.261 = arccos(((2*5^2)-8^2)/(2*5^2)).

How to calculate Outer Angle of Polygram given Chord Length?

With Edge Length of Polygram (l_e) & Chord Length of Polygram (l_c) we can find Outer Angle of Polygram given Chord Length using the formula - Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2)). This formula also uses Cosine (cos), Inverse Cosine (arccos) function(s).

What are the other ways to Calculate Outer Angle of Polygram?

Here are the different ways to Calculate Outer Angle of Polygram-

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

Can the Outer Angle of Polygram given Chord Length be negative?

No, the Outer Angle of Polygram given Chord Length, measured in Angle cannot be negative.

Which unit is used to measure Outer Angle of Polygram given Chord Length?

Outer Angle of Polygram given Chord Length is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Outer Angle of Polygram given Chord Length can be measured.

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