Inradius of Rhombus given Short Diagonal and Acute Angle Calculator

✖A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus.ⓘ Short Diagonal of Rhombus [d_Short]			+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 Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.ⓘ Inradius of Rhombus given Short Diagonal and Acute Angle [r_i]

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Inradius of Rhombus given Short Diagonal and Acute Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Inradius of Rhombus - (Measured in Meter) - The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.
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.
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

Short Diagonal of Rhombus: 8 Meter --> 8 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

r_i = d_Short/2*cos(∠_Acute/2) --> 8/2*cos(0.785398163397301/2)

Evaluating ... ...

r_i = 3.69551813004526

STEP 3: Convert Result to Output's Unit

3.69551813004526 Meter --> No Conversion Required

FINAL ANSWER

3.69551813004526 ≈ 3.695518 Meter <-- Inradius of Rhombus

(Calculation completed in 00.007 seconds)

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< Inradius of Rhombus Calculators

Inradius of Rhombus given both Diagonals

LaTeX Go Inradius of Rhombus = (Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(2*sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))

Inradius of Rhombus given Area and Acute Angle

LaTeX Go Inradius of Rhombus = sqrt(Area of Rhombus*sin(Acute Angle of Rhombus))/2

Inradius of Rhombus

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

Inradius of Rhombus given Area and Side

LaTeX Go Inradius of Rhombus = Area of Rhombus/(2*Side of Rhombus)

Inradius of Rhombus given Short Diagonal and Acute Angle Formula

LaTeX Go

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

What is a 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.

What is an Inscribed Circle?

In geometry, the incircle or inscribed circle of a polygon is the largest circle contained in the polygon; it touches (is tangent to) the many sides. The center of the incircle is called the polygon's incenter.The center of the incircle can be found as the intersection of the many internal angle bisectors.

How to Calculate Inradius of Rhombus given Short Diagonal and Acute Angle?

Inradius of Rhombus given Short Diagonal and Acute Angle calculator uses Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2) to calculate the Inradius of Rhombus, Inradius of Rhombus given Short Diagonal and Acute Angle is defined as the radius of the inscribed circle of the Rhombus, calculated using short diagonal and acute angle of the Rhombus. Inradius of Rhombus is denoted by r_i symbol.

How to calculate Inradius of Rhombus given Short Diagonal and Acute Angle using this online calculator? To use this online calculator for Inradius of Rhombus given Short Diagonal and Acute Angle, enter Short Diagonal of Rhombus (d_Short) & Acute Angle of Rhombus (∠_Acute) and hit the calculate button. Here is how the Inradius of Rhombus given Short Diagonal and Acute Angle calculation can be explained with given input values -> 3.695518 = 8/2*cos(0.785398163397301/2).

FAQ

What is Inradius of Rhombus given Short Diagonal and Acute Angle?

Inradius of Rhombus given Short Diagonal and Acute Angle is defined as the radius of the inscribed circle of the Rhombus, calculated using short diagonal and acute angle of the Rhombus and is represented as r_i = d_Short/2*cos(∠_Acute/2) or Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2). A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus & Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.

How to calculate Inradius of Rhombus given Short Diagonal and Acute Angle?

Inradius of Rhombus given Short Diagonal and Acute Angle is defined as the radius of the inscribed circle of the Rhombus, calculated using short diagonal and acute angle of the Rhombus is calculated using Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2). To calculate Inradius of Rhombus given Short Diagonal and Acute Angle, you need Short Diagonal of Rhombus (d_Short) & Acute Angle of Rhombus (∠_Acute). With our tool, you need to enter the respective value for Short Diagonal 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 Inradius of Rhombus?

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

Inradius of Rhombus = Area of Rhombus/(2*Side of Rhombus)
Inradius of Rhombus = sqrt(Area of Rhombus*sin(Acute Angle of Rhombus))/2
Inradius of Rhombus = (Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(2*sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))

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