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Spike Height of Fourstar given Inner Angle Formula

GoSpike Height of Fourstar Formula

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The Spike Height of Fourstar is the height of the isosceles triangles with respect to the unequal side, which are attached to the square of the Fourstar as the spikes. Check FAQs

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

h_Spike - Spike Height of Fourstar?l_e - Edge Length of Fourstar?∠_Inner - Inner Angle of Fourstar?

Spike Height of Fourstar given Inner Angle Example

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Here is how the Spike Height of Fourstar given Inner Angle equation looks like with Values.

Here is how the Spike Height of Fourstar given Inner Angle equation looks like with Units.

Here is how the Spike Height of Fourstar given Inner Angle equation looks like.

3.9668 = \frac{5}{2} \cdot \sqrt{2 \cdot (1 + \cos (75))}

3.9668m = \frac{5m}{2} \cdot \sqrt{2 \cdot (1 + \cos (75°))}

3.9668 = \frac{5}{2} \cdot \sqrt{2 \cdot (1 + \cos (75))}

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Spike Height of Fourstar given Inner Angle Solution

Follow our step by step solution on how to calculate Spike Height of Fourstar given Inner Angle?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h Spike = \frac{5m}{2} \cdot \sqrt{2 \cdot (1 + \cos (75°))}

Next Step Convert Units

∴

h Spike = \frac{5m}{2} \cdot \sqrt{2 \cdot (1 + \cos (1.309rad))}

Next Step Prepare to Evaluate

∴

h Spike = \frac{5}{2} \cdot \sqrt{2 \cdot (1 + \cos (1.309))}

Next Step Evaluate

∴

h Spike = 3.96676670145655m

LAST Step Rounding Answer

∴

h Spike = 3.9668m

Spike Height of Fourstar given Inner Angle Formula Elements

Variables

Functions

Spike Height of Fourstar

The Spike Height of Fourstar is the height of the isosceles triangles with respect to the unequal side, which are attached to the square of the Fourstar as the spikes.

Symbol: h_Spike

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Spike Height 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 Spike Height of Fourstar

Go Spike Height of Fourstar

h Spike = \sqrt{\frac{4 \cdot {l e}^{2} - {b Spike}^{2}}{4}}

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 Diameter of Fourstar given Edge Length and Inner Angle

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

Go Chord Length of Fourstar

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

How to Evaluate Spike Height of Fourstar given Inner Angle?

Spike Height of Fourstar given Inner Angle evaluator uses Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner Angle of Fourstar))) to evaluate the Spike Height of Fourstar, The Spike Height of Fourstar given Inner Angle formula is defined as the height of any isosceles triangles present in the Fourstar, calculated using inner angle. Spike Height of Fourstar is denoted by h_Spike symbol.

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

FAQs on Spike Height of Fourstar given Inner Angle

What is the formula to find Spike Height of Fourstar given Inner Angle?

The formula of Spike Height of Fourstar given Inner Angle is expressed as Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner Angle of Fourstar))). Here is an example- 3.966767 = 5/2*sqrt(2*(1+cos(1.3089969389955))).

How to calculate Spike Height of Fourstar given Inner Angle?

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

What are the other ways to Calculate Spike Height of Fourstar?

Here are the different ways to Calculate Spike Height of Fourstar-

Spike Height of Fourstar=sqrt((4*Edge Length of Fourstar^2-Spike Base of Fourstar^2)/4)

Can the Spike Height of Fourstar given Inner Angle be negative?

No, the Spike Height of Fourstar given Inner Angle, measured in Length cannot be negative.

Which unit is used to measure Spike Height of Fourstar given Inner Angle?

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

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