Short 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%

✖A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus.ⓘ Short Diagonal of Rhombus given Inradius [d_Short]

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Short Diagonal of Rhombus given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Diagonal of Rhombus = (2*Inradius of Rhombus)/cos(Acute Angle of Rhombus/2)
d_Short = (2*r_i)/cos(∠_Acute/2)
This formula uses 1 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)

Variables Used

Short Diagonal of Rhombus - (Measured in Meter) - A Short Diagonal of Rhombus is a length of the line joining the obtuse 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_Short = (2*r_i)/cos(∠_Acute/2) --> (2*3)/cos(0.785398163397301/2)

Evaluating ... ...

d_Short = 6.49435320175417

STEP 3: Convert Result to Output's Unit

6.49435320175417 Meter --> No Conversion Required

FINAL ANSWER

6.49435320175417 ≈ 6.494353 Meter <-- Short Diagonal of Rhombus

(Calculation completed in 00.004 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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< Short Diagonal of Rhombus Calculators

Short Diagonal of Rhombus given Long Diagonal and Acute Angle

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

Short Diagonal of Rhombus given Long Diagonal and Side

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

Short Diagonal of Rhombus given Obtuse Angle

LaTeX Go Short Diagonal of Rhombus = 2*Side of Rhombus*cos(Obtuse Angle of Rhombus/2)

Short Diagonal of Rhombus

LaTeX Go Short Diagonal of Rhombus = 2*Side of Rhombus*sin(Acute Angle of Rhombus/2)

Short Diagonal of Rhombus given Inradius Formula

LaTeX Go

Short Diagonal of Rhombus = (2*Inradius of Rhombus)/cos(Acute Angle of Rhombus/2)
d_Short = (2*r_i)/cos(∠_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 Short Diagonal of Rhombus given Inradius?

Short Diagonal of Rhombus given Inradius calculator uses Short Diagonal of Rhombus = (2*Inradius of Rhombus)/cos(Acute Angle of Rhombus/2) to calculate the Short Diagonal of Rhombus, The Short Diagonal of Rhombus given Inradius formula is defined as the line joining the obtuse angle corners, calculated using the inradius of the Rhombus. Short Diagonal of Rhombus is denoted by d_Short symbol.

How to calculate Short Diagonal of Rhombus given Inradius using this online calculator? To use this online calculator for Short 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 Short Diagonal of Rhombus given Inradius calculation can be explained with given input values -> 6.494353 = (2*3)/cos(0.785398163397301/2).

FAQ

What is Short Diagonal of Rhombus given Inradius?

The Short Diagonal of Rhombus given Inradius formula is defined as the line joining the obtuse angle corners, calculated using the inradius of the Rhombus and is represented as d_Short = (2*r_i)/cos(∠_Acute/2) or Short Diagonal of Rhombus = (2*Inradius of Rhombus)/cos(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 Short Diagonal of Rhombus given Inradius?

The Short Diagonal of Rhombus given Inradius formula is defined as the line joining the obtuse angle corners, calculated using the inradius of the Rhombus is calculated using Short Diagonal of Rhombus = (2*Inradius of Rhombus)/cos(Acute Angle of Rhombus/2). To calculate Short 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 Short Diagonal of Rhombus?

In this formula, Short Diagonal of Rhombus uses Inradius of Rhombus & Acute Angle of Rhombus. We can use 3 other way(s) to calculate the same, which is/are as follows -

Short Diagonal of Rhombus = 2*Side of Rhombus*cos(Obtuse Angle of Rhombus/2)
Short Diagonal of Rhombus = 2*Side of Rhombus*sin(Acute Angle of Rhombus/2)
Short Diagonal of Rhombus = Long Diagonal of Rhombus*tan(Acute Angle of Rhombus/2)

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