Base Length of Polygram given Inner Angle 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 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 [∠_Inner]			+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 given Inner Angle [l_Base]

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Base Length of Polygram given Inner Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Base Length of Polygram = Edge Length of Polygram*sqrt(2*(1-cos(Inner Angle of Polygram)))
l_Base = l_e*sqrt(2*(1-cos(∠_Inner)))
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)
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

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Polygram: 5 Meter --> 5 Meter No Conversion Required
Inner Angle of Polygram: 74 Degree --> 1.29154364647556 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_Base = l_e*sqrt(2*(1-cos(∠_Inner))) --> 5*sqrt(2*(1-cos(1.29154364647556)))

Evaluating ... ...

l_Base = 6.01815023151951

STEP 3: Convert Result to Output's Unit

6.01815023151951 Meter --> No Conversion Required

FINAL ANSWER

6.01815023151951 ≈ 6.01815 Meter <-- Base Length of Polygram

(Calculation completed in 00.020 seconds)

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IIT Madras (IIT Madras), Chennai

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< Base Length of Polygram Calculators

Base Length of Polygram given Inner Angle

LaTeX Go Base Length of Polygram = Edge Length of Polygram*sqrt(2*(1-cos(Inner Angle of Polygram)))

Base Length of Polygram given Spike Height

LaTeX Go Base Length of Polygram = 2*sqrt(Edge Length of Polygram^2-Spike Height of Polygram^2)

Base Length of Polygram given Inner Angle Formula

LaTeX Go

Base Length of Polygram = Edge Length of Polygram*sqrt(2*(1-cos(Inner Angle of Polygram)))
l_Base = l_e*sqrt(2*(1-cos(∠_Inner)))

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 Base Length of Polygram given Inner Angle?

Base Length of Polygram given Inner Angle calculator uses Base Length of Polygram = Edge Length of Polygram*sqrt(2*(1-cos(Inner Angle of Polygram))) to calculate the Base Length of Polygram, The Base Length of Polygram given Inner Angle formula is defined as the measurement of the baseline of the isosceles triangle (Spike of the Polygram) attached to the n-sided polygon of the Polygram and calculated using the inner angle. Base Length of Polygram is denoted by l_Base symbol.

How to calculate Base Length of Polygram given Inner Angle using this online calculator? To use this online calculator for Base Length of Polygram given Inner Angle, enter Edge Length of Polygram (l_e) & Inner Angle of Polygram (∠_Inner) and hit the calculate button. Here is how the Base Length of Polygram given Inner Angle calculation can be explained with given input values -> 6.01815 = 5*sqrt(2*(1-cos(1.29154364647556))).

FAQ

What is Base Length of Polygram given Inner Angle?

The Base Length of Polygram given Inner Angle formula is defined as the measurement of the baseline of the isosceles triangle (Spike of the Polygram) attached to the n-sided polygon of the Polygram and calculated using the inner angle and is represented as l_Base = l_e*sqrt(2*(1-cos(∠_Inner))) or Base Length of Polygram = Edge Length of Polygram*sqrt(2*(1-cos(Inner Angle of Polygram))). The Edge Length of Polygram is the length of any edge of the Polygram shape, from one end to other end & 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.

How to calculate Base Length of Polygram given Inner Angle?

The Base Length of Polygram given Inner Angle formula is defined as the measurement of the baseline of the isosceles triangle (Spike of the Polygram) attached to the n-sided polygon of the Polygram and calculated using the inner angle is calculated using Base Length of Polygram = Edge Length of Polygram*sqrt(2*(1-cos(Inner Angle of Polygram))). To calculate Base Length of Polygram given Inner Angle, you need Edge Length of Polygram (l_e) & Inner Angle of Polygram (∠_Inner). With our tool, you need to enter the respective value for Edge Length of Polygram & Inner Angle 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 Base Length of Polygram?

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

Base Length of Polygram = 2*sqrt(Edge Length of Polygram^2-Spike Height of Polygram^2)

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