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Obtuse Angle of Rhombus given Inradius Formula

GoObtuse Angle of Rhombus given Short Diagonal Formula

GoObtuse Angle of Rhombus given Long Diagonal Formula

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Obtuse Angle of Rhombus is the angle inside the Rhombus which is greater than 90 degree. Check FAQs

∠ Obtuse = π - a \sin (\frac{2 \cdot r i}{S})

∠_Obtuse - Obtuse Angle of Rhombus?r_i - Inradius of Rhombus?S - Side of Rhombus?π - Archimedes' constant?

Obtuse Angle of Rhombus given Inradius Example

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Here is how the Obtuse Angle of Rhombus given Inradius equation looks like with Values.

Here is how the Obtuse Angle of Rhombus given Inradius equation looks like with Units.

Here is how the Obtuse Angle of Rhombus given Inradius equation looks like.

143.1301 = 3.1416 - a \sin (\frac{2 \cdot 3}{10})

143.1301° = 3.1416 - a \sin (\frac{2 \cdot 3m}{10m})

143.1301 = 3.1416 - a \sin (\frac{2 \cdot 3}{10})

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Obtuse Angle of Rhombus given Inradius Solution

Follow our step by step solution on how to calculate Obtuse Angle of Rhombus given Inradius?

FIRST Step Consider the formula

∠ Obtuse = π - a \sin (\frac{2 \cdot r i}{S})

Next Step Substitute values of Variables

∴

∠ Obtuse = π - a \sin (\frac{2 \cdot 3m}{10m})

Next Step Substitute values of Constants

∴

∠ Obtuse = 3.1416 - a \sin (\frac{2 \cdot 3m}{10m})

Next Step Prepare to Evaluate

∴

∠ Obtuse = 3.1416 - a \sin (\frac{2 \cdot 3}{10})

Next Step Evaluate

∴

∠ Obtuse = 2.49809154479651rad

Next Step Convert to Output's Unit

∴

∠ Obtuse = 143.130102354183°

LAST Step Rounding Answer

∴

∠ Obtuse = 143.1301°

Obtuse Angle of Rhombus given Inradius Formula Elements

Variables

Constants

Functions

Obtuse Angle of Rhombus

Obtuse Angle of Rhombus is the angle inside the Rhombus which is greater than 90 degree.

Symbol: ∠_Obtuse

Measurement: AngleUnit: °

Note: Value should be between 90 to 180.

Formulas to find Obtuse Angle 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

Side of Rhombus

The Side of Rhombus is the length of any of the four edges.

Symbol: S

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side of Rhombus

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other Formulas to find Obtuse Angle of Rhombus

Go Obtuse Angle of Rhombus given Short Diagonal

∠ Obtuse = a \cos (\frac{{d Short}^{2}}{2 \cdot S^{2}} - 1)

Go Obtuse Angle of Rhombus given Long Diagonal

∠ Obtuse = a \cos (1 - \frac{{d Long}^{2}}{2 \cdot S^{2}})

Go Obtuse Angle of Rhombus given both Diagonals

∠ Obtuse = 2 \cdot a \cos (\frac{d Short}{\sqrt{{d Long}^{2} + {d Short}^{2}}})

Go Obtuse Angle of Rhombus given Area

∠ Obtuse = π - a \sin (\frac{A}{S^{2}})

How to Evaluate Obtuse Angle of Rhombus given Inradius?

Obtuse Angle of Rhombus given Inradius evaluator uses Obtuse Angle of Rhombus = pi-asin((2*Inradius of Rhombus)/Side of Rhombus) to evaluate the Obtuse Angle of Rhombus, The Obtuse Angle of Rhombus given Inradius is defined as the angle inside the Rhombus which is greater than 90 degrees, calculated using inradius of the Rhombus. Obtuse Angle of Rhombus is denoted by ∠_Obtuse symbol.

How to evaluate Obtuse Angle of Rhombus given Inradius using this online evaluator? To use this online evaluator for Obtuse Angle of Rhombus given Inradius, enter Inradius of Rhombus (r_i) & Side of Rhombus (S) and hit the calculate button.

FAQs on Obtuse Angle of Rhombus given Inradius

What is the formula to find Obtuse Angle of Rhombus given Inradius?

The formula of Obtuse Angle of Rhombus given Inradius is expressed as Obtuse Angle of Rhombus = pi-asin((2*Inradius of Rhombus)/Side of Rhombus). Here is an example- 8200.751 = pi-asin((2*3)/10).

How to calculate Obtuse Angle of Rhombus given Inradius?

With Inradius of Rhombus (r_i) & Side of Rhombus (S) we can find Obtuse Angle of Rhombus given Inradius using the formula - Obtuse Angle of Rhombus = pi-asin((2*Inradius of Rhombus)/Side of Rhombus). This formula also uses Archimedes' constant and , Sine (sin), Inverse Sine (asin) function(s).

What are the other ways to Calculate Obtuse Angle of Rhombus?

Here are the different ways to Calculate Obtuse Angle of Rhombus-

Obtuse Angle of Rhombus=acos(Short Diagonal of Rhombus^2/(2*Side of Rhombus^2)-1)
Obtuse Angle of Rhombus=acos(1-Long Diagonal of Rhombus^2/(2*Side of Rhombus^2))
Obtuse Angle of Rhombus=2*acos(Short Diagonal of Rhombus/sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))

Can the Obtuse Angle of Rhombus given Inradius be negative?

No, the Obtuse Angle of Rhombus given Inradius, measured in Angle cannot be negative.

Which unit is used to measure Obtuse Angle of Rhombus given Inradius?

Obtuse Angle of Rhombus given Inradius is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Obtuse Angle of Rhombus given Inradius can be measured.

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