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Inradius of Rhombus given Short Diagonal and Acute Angle Formula

GoInradius of Rhombus given Area and Side Formula

GoInradius of Rhombus given Area and Acute Angle Formula

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The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus. Check FAQs

r i = \frac{d Short}{2} \cdot \cos (\frac{∠ Acute}{2})

r_i - Inradius of Rhombus?d_Short - Short Diagonal of Rhombus?∠_Acute - Acute Angle of Rhombus?

Inradius of Rhombus given Short Diagonal and Acute Angle Example

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Here is how the Inradius of Rhombus given Short Diagonal and Acute Angle equation looks like with Values.

Here is how the Inradius of Rhombus given Short Diagonal and Acute Angle equation looks like with Units.

Here is how the Inradius of Rhombus given Short Diagonal and Acute Angle equation looks like.

3.6955 = \frac{8}{2} \cdot \cos (\frac{45}{2})

3.6955m = \frac{8m}{2} \cdot \cos (\frac{45°}{2})

3.6955 = \frac{8}{2} \cdot \cos (\frac{45}{2})

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Inradius of Rhombus given Short Diagonal and Acute Angle Solution

Follow our step by step solution on how to calculate Inradius of Rhombus given Short Diagonal and Acute Angle?

FIRST Step Consider the formula

r i = \frac{d Short}{2} \cdot \cos (\frac{∠ Acute}{2})

Next Step Substitute values of Variables

∴

r i = \frac{8m}{2} \cdot \cos (\frac{45°}{2})

Next Step Convert Units

∴

r i = \frac{8m}{2} \cdot \cos (\frac{0.7854rad}{2})

Next Step Prepare to Evaluate

∴

r i = \frac{8}{2} \cdot \cos (\frac{0.7854}{2})

Next Step Evaluate

∴

r i = 3.69551813004526m

LAST Step Rounding Answer

∴

r i = 3.6955m

Inradius of Rhombus given Short Diagonal and Acute Angle Formula Elements

Variables

Functions

Inradius of Rhombus

The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Rhombus

Short Diagonal of Rhombus

A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus.

Symbol: d_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Diagonal of Rhombus

Acute Angle of Rhombus

Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.

Symbol: ∠_Acute

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Acute Angle of Rhombus

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Inradius of Rhombus

Go Inradius of Rhombus given Area and Side

r i = \frac{A}{2 \cdot S}

Go Inradius of Rhombus given Area and Acute Angle

r i = \frac{\sqrt{A \cdot \sin (∠ Acute)}}{2}

Go Inradius of Rhombus given both Diagonals

r i = \frac{d Long \cdot d Short}{2 \cdot \sqrt{{d Long}^{2} + {d Short}^{2}}}

Go Inradius of Rhombus

r i = \frac{S \cdot \sin (∠ Acute)}{2}

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

Inradius of Rhombus given Short Diagonal and Acute Angle evaluator uses Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2) to evaluate 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 evaluate Inradius of Rhombus given Short Diagonal and Acute Angle using this online evaluator? To use this online evaluator 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.

FAQs on Inradius of Rhombus given Short Diagonal and Acute Angle

What is the formula to find Inradius of Rhombus given Short Diagonal and Acute Angle?

The formula of Inradius of Rhombus given Short Diagonal and Acute Angle is expressed as Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2). Here is an example- 3.695518 = 8/2*cos(0.785398163397301/2).

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

With Short Diagonal of Rhombus (d_Short) & Acute Angle of Rhombus (∠_Acute) we can find Inradius of Rhombus given Short Diagonal and Acute Angle using the formula - Inradius of Rhombus = Short Diagonal of Rhombus/2*cos(Acute Angle of Rhombus/2). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Inradius of Rhombus?

Here are the different ways to Calculate Inradius of Rhombus-

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))

Can the Inradius of Rhombus given Short Diagonal and Acute Angle be negative?

No, the Inradius of Rhombus given Short Diagonal and Acute Angle, measured in Length cannot be negative.

Which unit is used to measure Inradius of Rhombus given Short Diagonal and Acute Angle?

Inradius of Rhombus given Short Diagonal and Acute Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Rhombus given Short Diagonal and Acute Angle can be measured.

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