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Diameter of Fourstar given Edge Length and Inner Angle Formula

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The Diameter of Fourstar is the distance between the opposite spike tips of the Fourstar. Check FAQs

D = l e \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (∠ Inner)} + \sqrt{1 - \cos (∠ Inner)})

D - Diameter of Fourstar?l_e - Edge Length of Fourstar?∠_Inner - Inner Angle of Fourstar?

Diameter of Fourstar given Edge Length and Inner Angle Example

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Here is how the Diameter of Fourstar given Edge Length and Inner Angle equation looks like with Values.

Here is how the Diameter of Fourstar given Edge Length and Inner Angle equation looks like with Units.

Here is how the Diameter of Fourstar given Edge Length and Inner Angle equation looks like.

14.0211 = 5 \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (75)} + \sqrt{1 - \cos (75)})

14.0211m = 5m \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (75°)} + \sqrt{1 - \cos (75°)})

14.0211 = 5 \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (75)} + \sqrt{1 - \cos (75)})

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Diameter of Fourstar given Edge Length and Inner Angle Solution

Follow our step by step solution on how to calculate Diameter of Fourstar given Edge Length and Inner Angle?

FIRST Step Consider the formula

D = l e \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (∠ Inner)} + \sqrt{1 - \cos (∠ Inner)})

Next Step Substitute values of Variables

∴

D = 5m \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (75°)} + \sqrt{1 - \cos (75°)})

Next Step Convert Units

∴

D = 5m \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (1.309rad)} + \sqrt{1 - \cos (1.309rad)})

Next Step Prepare to Evaluate

∴

D = 5 \cdot \sqrt{2} \cdot (\sqrt{1 + \cos (1.309)} + \sqrt{1 - \cos (1.309)})

Next Step Evaluate

∴

D = 14.0211476929993m

LAST Step Rounding Answer

∴

D = 14.0211m

Diameter of Fourstar given Edge Length and Inner Angle Formula Elements

Variables

Functions

Diameter of Fourstar

The Diameter of Fourstar is the distance between the opposite spike tips of the Fourstar.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Fourstar

Edge Length of Fourstar

The Edge Length of Fourstar is the length of any edge of the Fourstar 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 Fourstar

Inner Angle of Fourstar

The Inner Angle of Fourstar is the unequal angle of the isosceles triangle that attached to the square or the angle between the edges which form the triangular spike, of the Fourstar.

Symbol: ∠_Inner

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Inner Angle of Fourstar

cos

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

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Diameter of Fourstar

Go Diameter of Fourstar

D = 2 \cdot h Spike + b Spike

Other formulas in Fourstar category

Go Outer Angle of Fourstar

∠ Outer = ∠ Inner + \frac{π}{2}

Go Spike Base of Fourstar

b Spike = \sqrt{2 \cdot {l e}^{2} \cdot (1 - \cos (∠ Inner))}

Go Spike Height of Fourstar given Inner Angle

h Spike = \frac{l e}{2} \cdot \sqrt{2 \cdot (1 + \cos (∠ Inner))}

Go Chord Length of Fourstar

l c = \sqrt{2 \cdot {l e}^{2} \cdot (1 - \cos (∠ Outer))}

How to Evaluate Diameter of Fourstar given Edge Length and Inner Angle?

Diameter of Fourstar given Edge Length and Inner Angle evaluator uses Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar))) to evaluate the Diameter of Fourstar, The Diameter of Fourstar given Edge Length and Inner Angle formula is defined as the distance between the sharp tips of any two opposite triangular petals of a Fourstar, calculated using edge length and inner angle. Diameter of Fourstar is denoted by D symbol.

How to evaluate Diameter of Fourstar given Edge Length and Inner Angle using this online evaluator? To use this online evaluator for Diameter of Fourstar given Edge Length and Inner Angle, enter Edge Length of Fourstar (l_e) & Inner Angle of Fourstar (∠_Inner) and hit the calculate button.

FAQs on Diameter of Fourstar given Edge Length and Inner Angle

What is the formula to find Diameter of Fourstar given Edge Length and Inner Angle?

The formula of Diameter of Fourstar given Edge Length and Inner Angle is expressed as Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar))). Here is an example- 14.02115 = 5*sqrt(2)*(sqrt(1+cos(1.3089969389955))+sqrt(1-cos(1.3089969389955))).

How to calculate Diameter of Fourstar given Edge Length and Inner Angle?

With Edge Length of Fourstar (l_e) & Inner Angle of Fourstar (∠_Inner) we can find Diameter of Fourstar given Edge Length and Inner Angle using the formula - Diameter of Fourstar = Edge Length of Fourstar*sqrt(2)*(sqrt(1+cos(Inner Angle of Fourstar))+sqrt(1-cos(Inner Angle of Fourstar))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Diameter of Fourstar?

Here are the different ways to Calculate Diameter of Fourstar-

Diameter of Fourstar=2*Spike Height of Fourstar+Spike Base of Fourstar

Can the Diameter of Fourstar given Edge Length and Inner Angle be negative?

No, the Diameter of Fourstar given Edge Length and Inner Angle, measured in Length cannot be negative.

Which unit is used to measure Diameter of Fourstar given Edge Length and Inner Angle?

Diameter of Fourstar given Edge Length and Inner Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diameter of Fourstar given Edge Length and Inner Angle can be measured.

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