Spike Height of Fourstar given Inner Angle 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 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.ⓘ Inner Angle of Fourstar [∠_Inner]			+10% -10%

✖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.ⓘ Spike Height of Fourstar given Inner Angle [h_Spike]

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Formula

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Spike Height of Fourstar given Inner Angle

Formula

`"h"_{"Spike"} = "l"_{"e"}/2*sqrt(2*(1+cos("∠"_{"Inner"})))`

Example

`"3.966767m"="5m"/2*sqrt(2*(1+cos("75°")))`

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Spike Height of Fourstar given Inner Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Spike Height of Fourstar - (Measured in Meter) - 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.
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.
Inner Angle of Fourstar - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Fourstar: 5 Meter --> 5 Meter No Conversion Required
Inner Angle of Fourstar: 75 Degree --> 1.3089969389955 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_Spike = l_e/2*sqrt(2*(1+cos(∠_Inner))) --> 5/2*sqrt(2*(1+cos(1.3089969389955)))

Evaluating ... ...

h_Spike = 3.96676670145655

STEP 3: Convert Result to Output's Unit

3.96676670145655 Meter --> No Conversion Required

FINAL ANSWER

3.96676670145655 ≈ 3.966767 Meter <-- Spike Height of Fourstar

(Calculation completed in 00.004 seconds)

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< 10+ Fourstar Calculators

Diameter of Fourstar given Edge Length and Inner Angle

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

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

Chord Length of Fourstar

Go Chord Length of Fourstar = sqrt(2*Edge Length of Fourstar^2*(1-cos(Outer Angle of Fourstar)))

Spike Base of Fourstar

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

Area of Fourstar

Go Area of Fourstar = (2*Spike Height of Fourstar*Spike Base of Fourstar)+Spike Base of Fourstar^2

Spike Height of Fourstar

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

Spike Base of Fourstar given Diameter

Go Spike Base of Fourstar = Diameter of Fourstar-2*Spike Height of Fourstar

Diameter of Fourstar

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

Outer Angle of Fourstar

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

Perimeter of Fourstar

Go Perimeter of Fourstar = 8*Edge Length of Fourstar

Spike Height of Fourstar given Inner Angle Formula

Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner Angle of Fourstar)))
h_Spike = l_e/2*sqrt(2*(1+cos(∠_Inner)))

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 Spike Height of Fourstar given Inner Angle?

Spike Height of Fourstar given Inner Angle calculator uses Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner Angle of Fourstar))) to calculate 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 calculate Spike Height of Fourstar given Inner Angle using this online calculator? To use this online calculator 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. Here is how the Spike Height of Fourstar given Inner Angle calculation can be explained with given input values -> 3.966767 = 5/2*sqrt(2*(1+cos(1.3089969389955))).

FAQ

What is Spike Height of Fourstar given Inner Angle?

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 and is represented as h_Spike = l_e/2*sqrt(2*(1+cos(∠_Inner))) or Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner 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 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.

How to calculate Spike Height of Fourstar given Inner Angle?

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 is calculated using Spike Height of Fourstar = Edge Length of Fourstar/2*sqrt(2*(1+cos(Inner Angle of Fourstar))). To calculate Spike Height of Fourstar given Inner Angle, you need Edge Length of Fourstar (l_e) & Inner Angle of Fourstar (∠_Inner). With our tool, you need to enter the respective value for Edge Length of Fourstar & Inner Angle of Fourstar 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 Spike Height of Fourstar?

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

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

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