Long Diagonal of Rhombus given Inradius Calculator

✖The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.ⓘ Inradius of Rhombus [r_i]			+10% -10%
✖Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.ⓘ Acute Angle of Rhombus [∠_Acute]			+10% -10%

✖The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.ⓘ Long Diagonal of Rhombus given Inradius [d_Long]

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Formula

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Long Diagonal of Rhombus given Inradius

Formula

`"d"_{"Long"} = (2*"r"_{"i"})/sin("∠"_{"Acute"}/2)`

Example

`"15.67876m"=(2*"3m")/sin("45°"/2)`

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Long Diagonal of Rhombus given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2)
d_Long = (2*r_i)/sin(∠_Acute/2)
This formula uses 1 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Long Diagonal of Rhombus - (Measured in Meter) - The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.
Inradius of Rhombus - (Measured in Meter) - The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.
Acute Angle of Rhombus - (Measured in Radian) - Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.

STEP 1: Convert Input(s) to Base Unit

Inradius of Rhombus: 3 Meter --> 3 Meter No Conversion Required
Acute Angle of Rhombus: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Long = (2*r_i)/sin(∠_Acute/2) --> (2*3)/sin(0.785398163397301/2)

Evaluating ... ...

d_Long = 15.6787555785193

STEP 3: Convert Result to Output's Unit

15.6787555785193 Meter --> No Conversion Required

FINAL ANSWER

15.6787555785193 ≈ 15.67876 Meter <-- Long Diagonal of Rhombus

(Calculation completed in 00.020 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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Mumbai University (DJSCE), Mumbai

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< 9 Long Diagonal of Rhombus Calculators

Long Diagonal of Rhombus given Area

Go Long Diagonal of Rhombus = Area of Rhombus/(Side of Rhombus*sin(Acute Angle of Rhombus/2))

Long Diagonal of Rhombus given Short Diagonal and Acute Angle

Go Long Diagonal of Rhombus = Short Diagonal of Rhombus/tan(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus given Short Diagonal and Side

Go Long Diagonal of Rhombus = sqrt(4*Side of Rhombus^2-Short Diagonal of Rhombus^2)

Long Diagonal of Rhombus given Inradius

Go Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus given Perimeter

Go Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus given Obtuse angle

Go Long Diagonal of Rhombus = 2*Side of Rhombus*sin(Obtuse Angle of Rhombus/2)

Long Diagonal of Rhombus given Height

Go Long Diagonal of Rhombus = Height of Rhombus/sin(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus

Go Long Diagonal of Rhombus = 2*Side of Rhombus*cos(Acute Angle of Rhombus/2)

Long Diagonal of Rhombus given Area and Short Diagonal

Go Long Diagonal of Rhombus = (2*Area of Rhombus)/(Short Diagonal of Rhombus)

Long Diagonal of Rhombus given Inradius Formula

Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2)
d_Long = (2*r_i)/sin(∠_Acute/2)

What is Rhombus?

A Rhombus is a special case of a parallelogram. In a Rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a Rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or Rhombus diamond. The plural form of a Rhombus is Rhombi or Rhombuses.

How to Calculate Long Diagonal of Rhombus given Inradius?

Long Diagonal of Rhombus given Inradius calculator uses Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2) to calculate the Long Diagonal of Rhombus, The Long Diagonal of Rhombus given Inradius formula is defined as the length of the line joining the acute angle corners of the Rhombus, calculated using the inradius of the Rhombus. Long Diagonal of Rhombus is denoted by d_Long symbol.

How to calculate Long Diagonal of Rhombus given Inradius using this online calculator? To use this online calculator for Long Diagonal of Rhombus given Inradius, enter Inradius of Rhombus (r_i) & Acute Angle of Rhombus (∠_Acute) and hit the calculate button. Here is how the Long Diagonal of Rhombus given Inradius calculation can be explained with given input values -> 15.67876 = (2*3)/sin(0.785398163397301/2).

FAQ

What is Long Diagonal of Rhombus given Inradius?

The Long Diagonal of Rhombus given Inradius formula is defined as the length of the line joining the acute angle corners of the Rhombus, calculated using the inradius of the Rhombus and is represented as d_Long = (2*r_i)/sin(∠_Acute/2) or Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2). The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus & Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.

How to calculate Long Diagonal of Rhombus given Inradius?

The Long Diagonal of Rhombus given Inradius formula is defined as the length of the line joining the acute angle corners of the Rhombus, calculated using the inradius of the Rhombus is calculated using Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2). To calculate Long Diagonal of Rhombus given Inradius, you need Inradius of Rhombus (r_i) & Acute Angle of Rhombus (∠_Acute). With our tool, you need to enter the respective value for Inradius of Rhombus & Acute Angle of Rhombus 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 Long Diagonal of Rhombus?

In this formula, Long Diagonal of Rhombus uses Inradius of Rhombus & Acute Angle of Rhombus. We can use 8 other way(s) to calculate the same, which is/are as follows -

Long Diagonal of Rhombus = 2*Side of Rhombus*sin(Obtuse Angle of Rhombus/2)
Long Diagonal of Rhombus = 2*Side of Rhombus*cos(Acute Angle of Rhombus/2)
Long Diagonal of Rhombus = Short Diagonal of Rhombus/tan(Acute Angle of Rhombus/2)
Long Diagonal of Rhombus = sqrt(4*Side of Rhombus^2-Short Diagonal of Rhombus^2)
Long Diagonal of Rhombus = (2*Area of Rhombus)/(Short Diagonal of Rhombus)
Long Diagonal of Rhombus = Area of Rhombus/(Side of Rhombus*sin(Acute Angle of Rhombus/2))
Long Diagonal of Rhombus = Perimeter of Rhombus/2*cos(Acute Angle of Rhombus/2)
Long Diagonal of Rhombus = Height of Rhombus/sin(Acute Angle of Rhombus/2)

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