Short Sides of Arrow Hexagon Calculator

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✖Gap Width of Arrow Hexagon is the measurement of the base of the smaller isosceles triangle, removed at the center of the base of Arrow Hexagon.ⓘ Gap Width of Arrow Hexagon [w_Gap]			+10% -10%
✖Top Angle of Arrow Hexagon is defined as the angle between the two sides of equal length of the Arrow Hexagon.ⓘ Top Angle of Arrow Hexagon [∠_Top]			+10% -10%

✖Short Side of Arrow Hexagon is the measurement of the length of the shortest side of the Arrow Hexagon.ⓘ Short Sides of Arrow Hexagon [S_Short]

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Formula

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Short Sides of Arrow Hexagon

Formula

`"S"_{"Short"} = sqrt(("w"_{"Gap"}^2)/(2*(1-cos("∠"_{"Top"}))))`

Example

`"6.532815m"=sqrt((("5m")^2)/(2*(1-cos("45°"))))`

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Short Sides of Arrow Hexagon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Side of Arrow Hexagon = sqrt((Gap Width of Arrow Hexagon^2)/(2*(1-cos(Top Angle of Arrow Hexagon))))
S_Short = sqrt((w_Gap^2)/(2*(1-cos(∠_Top))))
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

Short Side of Arrow Hexagon - (Measured in Meter) - Short Side of Arrow Hexagon is the measurement of the length of the shortest side of the Arrow Hexagon.
Gap Width of Arrow Hexagon - (Measured in Meter) - Gap Width of Arrow Hexagon is the measurement of the base of the smaller isosceles triangle, removed at the center of the base of Arrow Hexagon.
Top Angle of Arrow Hexagon - (Measured in Radian) - Top Angle of Arrow Hexagon is defined as the angle between the two sides of equal length of the Arrow Hexagon.

STEP 1: Convert Input(s) to Base Unit

Gap Width of Arrow Hexagon: 5 Meter --> 5 Meter No Conversion Required
Top Angle of Arrow Hexagon: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_Short = sqrt((w_Gap^2)/(2*(1-cos(∠_Top)))) --> sqrt((5^2)/(2*(1-cos(0.785398163397301))))

Evaluating ... ...

S_Short = 6.53281482438304

STEP 3: Convert Result to Output's Unit

6.53281482438304 Meter --> No Conversion Required

FINAL ANSWER

6.53281482438304 ≈ 6.532815 Meter <-- Short Side of Arrow Hexagon

(Calculation completed in 00.004 seconds)

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Created by Prachi

Kamala Nehru College, University of Delhi (KNC), New Delhi

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Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< 9 Arrow Hexagon Calculators

Area of Arrow Hexagon

Go Area of Arrow Hexagon = ((Total Height of Arrow Hexagon*Base Width of Arrow Hexagon)-(Gap Height of Arrow Hexagon*Gap Width of Arrow Hexagon))/2

Short Sides of Arrow Hexagon

Go Short Side of Arrow Hexagon = sqrt((Gap Width of Arrow Hexagon^2)/(2*(1-cos(Top Angle of Arrow Hexagon))))

Base Width of Arrow Hexagon

Go Base Width of Arrow Hexagon = sqrt(2*Long Side of Arrow Hexagon^2*(1-cos(Top Angle of Arrow Hexagon)))

Perimeter of Arrow Hexagon

Go Perimeter of Arrow Hexagon = 2*(Long Side of Arrow Hexagon+Base Side of Arrow Hexagon+Short Side of Arrow Hexagon)

Total Height of Arrow Hexagon

Go Total Height of Arrow Hexagon = sqrt(((4*Long Side of Arrow Hexagon^2)-Base Width of Arrow Hexagon^2)/4)

Gap Height of Arrow Hexagon

Go Gap Height of Arrow Hexagon = sqrt(((4*Short Side of Arrow Hexagon^2)-Gap Width of Arrow Hexagon^2)/4)

Gap Height of Arrow Hexagon given Total Height

Go Gap Height of Arrow Hexagon = Total Height of Arrow Hexagon-Top Height of Arrow Hexagon

Top Height of Arrow Hexagon

Go Top Height of Arrow Hexagon = Total Height of Arrow Hexagon-Gap Height of Arrow Hexagon

Base Width of Arrow Hexagon given Base Side

Go Base Width of Arrow Hexagon = 2*Base Side of Arrow Hexagon+Gap Width of Arrow Hexagon

Short Sides of Arrow Hexagon Formula

Short Side of Arrow Hexagon = sqrt((Gap Width of Arrow Hexagon^2)/(2*(1-cos(Top Angle of Arrow Hexagon))))
S_Short = sqrt((w_Gap^2)/(2*(1-cos(∠_Top))))

What is an Arrow Hexagon?

An Arrow Hexagon is actually an isosceles triangle, from which a smaller yet similar isosceles triangle is withdrawn at the center of its base. The resultant is a concave hexagon with three pairs of sides.

How to Calculate Short Sides of Arrow Hexagon?

Short Sides of Arrow Hexagon calculator uses Short Side of Arrow Hexagon = sqrt((Gap Width of Arrow Hexagon^2)/(2*(1-cos(Top Angle of Arrow Hexagon)))) to calculate the Short Side of Arrow Hexagon, Short Sides of Arrow Hexagon formula is defined as the measurement of the length of the two sides of equal length of the isosceles triangle removed at the base. Short Side of Arrow Hexagon is denoted by S_Short symbol.

How to calculate Short Sides of Arrow Hexagon using this online calculator? To use this online calculator for Short Sides of Arrow Hexagon, enter Gap Width of Arrow Hexagon (w_Gap) & Top Angle of Arrow Hexagon (∠_Top) and hit the calculate button. Here is how the Short Sides of Arrow Hexagon calculation can be explained with given input values -> 6.532815 = sqrt((5^2)/(2*(1-cos(0.785398163397301)))).

FAQ

What is Short Sides of Arrow Hexagon?

Short Sides of Arrow Hexagon formula is defined as the measurement of the length of the two sides of equal length of the isosceles triangle removed at the base and is represented as S_Short = sqrt((w_Gap^2)/(2*(1-cos(∠_Top)))) or Short Side of Arrow Hexagon = sqrt((Gap Width of Arrow Hexagon^2)/(2*(1-cos(Top Angle of Arrow Hexagon)))). Gap Width of Arrow Hexagon is the measurement of the base of the smaller isosceles triangle, removed at the center of the base of Arrow Hexagon & Top Angle of Arrow Hexagon is defined as the angle between the two sides of equal length of the Arrow Hexagon.

How to calculate Short Sides of Arrow Hexagon?

Short Sides of Arrow Hexagon formula is defined as the measurement of the length of the two sides of equal length of the isosceles triangle removed at the base is calculated using Short Side of Arrow Hexagon = sqrt((Gap Width of Arrow Hexagon^2)/(2*(1-cos(Top Angle of Arrow Hexagon)))). To calculate Short Sides of Arrow Hexagon, you need Gap Width of Arrow Hexagon (w_Gap) & Top Angle of Arrow Hexagon (∠_Top). With our tool, you need to enter the respective value for Gap Width of Arrow Hexagon & Top Angle of Arrow Hexagon 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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