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Chord Length of Fourstar Calculator

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✖The Edge Length of Fourstar is the length of any edge of the Fourstar shape from one end to other end.ⓘ Edge Length of Fourstar [l_e]			+10% -10%
✖The Outer Angle of Fourstar is the angle between adjacent isosceles triangle or the triangular spikes that attached to the square of the Fourstar.ⓘ Outer Angle of Fourstar [∠_Outer]			+10% -10%

✖The Chord Length of Fourstar is the distance between any two adjacent spike tips of the Fourstar from one tip to other tip.ⓘ Chord Length of Fourstar [l_c]

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Chord Length of Fourstar Solution

STEP 0: Pre-Calculation Summary

Formula Used

Chord Length of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Outer Angle of Fourstar)))
l_c = sqrt(2*l_e^2*(1-cos(∠_Outer)))
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

Chord Length of Fourstar - (Measured in Meter) - The Chord Length of Fourstar is the distance between any two adjacent spike tips of the Fourstar from one tip to other tip.
Edge Length of Fourstar - (Measured in Meter) - The Edge Length of Fourstar is the length of any edge of the Fourstar shape from one end to other end.
Outer Angle of Fourstar - (Measured in Radian) - The Outer Angle of Fourstar is the angle between adjacent isosceles triangle or the triangular spikes that attached to the square of the Fourstar.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Fourstar: 5 Meter --> 5 Meter No Conversion Required
Outer Angle of Fourstar: 165 Degree --> 2.8797932657901 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = sqrt(2*l_e^2*(1-cos(∠_Outer))) --> sqrt(2*5^2*(1-cos(2.8797932657901)))

Evaluating ... ...

l_c = 9.91444861373775

STEP 3: Convert Result to Output's Unit

9.91444861373775 Meter --> No Conversion Required

FINAL ANSWER

9.91444861373775 ≈ 9.914449 Meter <-- Chord Length of Fourstar

(Calculation completed in 00.020 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

Jaseem K has created this Calculator and 100+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Fourstar Calculators

Diameter of Fourstar given Edge Length and Inner Angle

LaTeX Go Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar)))

Spike Height of Fourstar given Inner Angle

LaTeX Go Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner Angle of Fourstar)))

Spike Base of Fourstar

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

Outer Angle of Fourstar

LaTeX Go Outer Angle of Fourstar = Inner Angle of Fourstar+pi/2

Chord Length of Fourstar Formula

LaTeX Go

Chord Length of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Outer Angle of Fourstar)))
l_c = sqrt(2*l_e^2*(1-cos(∠_Outer)))

What is a Fourstar?

Fourstar is basically a four petal star shape. More clearly, it consists of a square and four identical triangles each having one side equal to the side length of the square. Each triangle is joined to the square with side of triangle with same length as the square coincide each other.

How to Calculate Chord Length of Fourstar?

Chord Length of Fourstar calculator uses Chord Length of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Outer Angle of Fourstar))) to calculate the Chord Length of Fourstar, The Chord Length of Fourstar formula is defined as the length of the line joining adjacent triangular tips of the given Fourstar. Chord Length of Fourstar is denoted by l_c symbol.

How to calculate Chord Length of Fourstar using this online calculator? To use this online calculator for Chord Length of Fourstar, enter Edge Length of Fourstar (l_e) & Outer Angle of Fourstar (∠_Outer) and hit the calculate button. Here is how the Chord Length of Fourstar calculation can be explained with given input values -> 9.914449 = sqrt(2*5^2*(1-cos(2.8797932657901))).

FAQ

What is Chord Length of Fourstar?

The Chord Length of Fourstar formula is defined as the length of the line joining adjacent triangular tips of the given Fourstar and is represented as l_c = sqrt(2*l_e^2*(1-cos(∠_Outer))) or Chord Length of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Outer Angle of Fourstar))). The Edge Length of Fourstar is the length of any edge of the Fourstar shape from one end to other end & The Outer Angle of Fourstar is the angle between adjacent isosceles triangle or the triangular spikes that attached to the square of the Fourstar.

How to calculate Chord Length of Fourstar?

The Chord Length of Fourstar formula is defined as the length of the line joining adjacent triangular tips of the given Fourstar is calculated using Chord Length of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Outer Angle of Fourstar))). To calculate Chord Length of Fourstar, you need Edge Length of Fourstar (l_e) & Outer Angle of Fourstar (∠_Outer). With our tool, you need to enter the respective value for Edge Length of Fourstar & Outer Angle of Fourstar and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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