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Long Diagonal of Rhombus given Inradius Formula

GoLong Diagonal of Rhombus given Obtuse angle Formula

GoLong Diagonal of Rhombus Formula

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The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus. Check FAQs

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

d_Long - Long Diagonal of Rhombus?r_i - Inradius of Rhombus?∠_Acute - Acute Angle of Rhombus?

Long Diagonal of Rhombus given Inradius Example

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Here is how the Long Diagonal of Rhombus given Inradius equation looks like with Values.

Here is how the Long Diagonal of Rhombus given Inradius equation looks like with Units.

Here is how the Long Diagonal of Rhombus given Inradius equation looks like.

15.6788 = \frac{2 \cdot 3}{\sin (\frac{45}{2})}

15.6788m = \frac{2 \cdot 3m}{\sin (\frac{45°}{2})}

15.6788 = \frac{2 \cdot 3}{\sin (\frac{45}{2})}

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Long Diagonal of Rhombus given Inradius Solution

Follow our step by step solution on how to calculate Long Diagonal of Rhombus given Inradius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Long = \frac{2 \cdot 3m}{\sin (\frac{45°}{2})}

Next Step Convert Units

∴

d Long = \frac{2 \cdot 3m}{\sin (\frac{0.7854rad}{2})}

Next Step Prepare to Evaluate

∴

d Long = \frac{2 \cdot 3}{\sin (\frac{0.7854}{2})}

Next Step Evaluate

∴

d Long = 15.6787555785193m

LAST Step Rounding Answer

∴

d Long = 15.6788m

Long Diagonal of Rhombus given Inradius Formula Elements

Variables

Functions

Long Diagonal of Rhombus

The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.

Symbol: d_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Diagonal of Rhombus

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

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

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.

Syntax: sin(Angle)

Other Formulas to find Long Diagonal of Rhombus

Go Long Diagonal of Rhombus given Obtuse angle

d Long = 2 \cdot S \cdot \sin (\frac{∠ Obtuse}{2})

Go Long Diagonal of Rhombus

d Long = 2 \cdot S \cdot \cos (\frac{∠ Acute}{2})

Go Long Diagonal of Rhombus given Short Diagonal and Acute Angle

d Long = \frac{d Short}{\tan (\frac{∠ Acute}{2})}

Go Long Diagonal of Rhombus given Short Diagonal and Side

d Long = \sqrt{4 \cdot S^{2} - {d Short}^{2}}

How to Evaluate Long Diagonal of Rhombus given Inradius?

Long Diagonal of Rhombus given Inradius evaluator uses Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2) to evaluate 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 evaluate Long Diagonal of Rhombus given Inradius using this online evaluator? To use this online evaluator for Long Diagonal of Rhombus given Inradius, enter Inradius of Rhombus (r_i) & Acute Angle of Rhombus (∠_Acute) and hit the calculate button.

FAQs on Long Diagonal of Rhombus given Inradius

What is the formula to find Long Diagonal of Rhombus given Inradius?

The formula of Long Diagonal of Rhombus given Inradius is expressed as Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2). Here is an example- 15.67876 = (2*3)/sin(0.785398163397301/2).

How to calculate Long Diagonal of Rhombus given Inradius?

With Inradius of Rhombus (r_i) & Acute Angle of Rhombus (∠_Acute) we can find Long Diagonal of Rhombus given Inradius using the formula - Long Diagonal of Rhombus = (2*Inradius of Rhombus)/sin(Acute Angle of Rhombus/2). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Long Diagonal of Rhombus?

Here are the different ways to Calculate Long Diagonal of Rhombus-

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)

Can the Long Diagonal of Rhombus given Inradius be negative?

No, the Long Diagonal of Rhombus given Inradius, measured in Length cannot be negative.

Which unit is used to measure Long Diagonal of Rhombus given Inradius?

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

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