Inner Angle of Polygram given Base 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 Base Length of Polygram is the length of the unequal side of the isosceles triangle which forms as the spikes of the Polygram or the side length of the polygon of Polygram.ⓘ Base Length of Polygram [l_Base]			+10% -10%

✖The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.ⓘ Inner Angle of Polygram given Base Length [∠_Inner]

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Inner Angle of Polygram given Base Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base Length of Polygram^2)/(2*Edge Length of Polygram^2))
∠_Inner = arccos(((2*l_e^2)-l_Base^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

Inner Angle of Polygram - (Measured in Radian) - The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of 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.
Base Length of Polygram - (Measured in Meter) - The Base Length of Polygram is the length of the unequal side of the isosceles triangle which forms as the spikes of the Polygram or the side length of the polygon of Polygram.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Polygram: 5 Meter --> 5 Meter No Conversion Required
Base Length of Polygram: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Inner = arccos(((2*l_e^2)-l_Base^2)/(2*l_e^2)) --> arccos(((2*5^2)-6^2)/(2*5^2))

Evaluating ... ...

∠_Inner = 1.28700221758657

STEP 3: Convert Result to Output's Unit

1.28700221758657 Radian -->73.7397952917019 Degree (Check conversion here)

FINAL ANSWER

73.7397952917019 ≈ 73.7398 Degree <-- Inner Angle of Polygram

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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The National Institute of Engineering (NIE), Mysuru

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< Inner Angle of Polygram Calculators

Inner Angle of Polygram given Base Length

LaTeX Go Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base Length of Polygram^2)/(2*Edge Length of Polygram^2))

Inner Angle of Polygram given Outer Angle

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

Inner Angle of Polygram given Base Length Formula

LaTeX Go

Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base Length of Polygram^2)/(2*Edge Length of Polygram^2))
∠_Inner = arccos(((2*l_e^2)-l_Base^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 Inner Angle of Polygram given Base Length?

Inner Angle of Polygram given Base Length calculator uses Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base Length of Polygram^2)/(2*Edge Length of Polygram^2)) to calculate the Inner Angle of Polygram, The Inner Angle of Polygram given Base Length formula is defined as the unequal angle of the isosceles triangles which are attached to the polygon of the Polygram and calculated using base length. Inner Angle of Polygram is denoted by ∠_Inner symbol.

How to calculate Inner Angle of Polygram given Base Length using this online calculator? To use this online calculator for Inner Angle of Polygram given Base Length, enter Edge Length of Polygram (l_e) & Base Length of Polygram (l_Base) and hit the calculate button. Here is how the Inner Angle of Polygram given Base Length calculation can be explained with given input values -> 4224.979 = arccos(((2*5^2)-6^2)/(2*5^2)).

FAQ

What is Inner Angle of Polygram given Base Length?

The Inner Angle of Polygram given Base Length formula is defined as the unequal angle of the isosceles triangles which are attached to the polygon of the Polygram and calculated using base length and is represented as ∠_Inner = arccos(((2*l_e^2)-l_Base^2)/(2*l_e^2)) or Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base 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 Base Length of Polygram is the length of the unequal side of the isosceles triangle which forms as the spikes of the Polygram or the side length of the polygon of Polygram.

How to calculate Inner Angle of Polygram given Base Length?

The Inner Angle of Polygram given Base Length formula is defined as the unequal angle of the isosceles triangles which are attached to the polygon of the Polygram and calculated using base length is calculated using Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base Length of Polygram^2)/(2*Edge Length of Polygram^2)). To calculate Inner Angle of Polygram given Base Length, you need Edge Length of Polygram (l_e) & Base Length of Polygram (l_Base). With our tool, you need to enter the respective value for Edge Length of Polygram & Base 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 Inner Angle of Polygram?

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

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

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