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Acute Angle of Rhombus given Inradius Formula

GoAcute Angle of Rhombus given Long Diagonal Formula

GoAcute Angle of Rhombus given Short Diagonal Formula

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

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

∠_Acute - Acute Angle of Rhombus?r_i - Inradius of Rhombus?S - Side of Rhombus?

Acute Angle of Rhombus given Inradius Example

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

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

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

36.8699 = a \sin (\frac{2 \cdot 3}{10})

36.8699° = a \sin (\frac{2 \cdot 3m}{10m})

36.8699 = a \sin (\frac{2 \cdot 3}{10})

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Acute Angle of Rhombus given Inradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

∠ Acute = a \sin (\frac{2 \cdot 3m}{10m})

Next Step Prepare to Evaluate

∴

∠ Acute = a \sin (\frac{2 \cdot 3}{10})

Next Step Evaluate

∴

∠ Acute = 0.643501108793284rad

Next Step Convert to Output's Unit

∴

∠ Acute = 36.869897645851°

LAST Step Rounding Answer

∴

∠ Acute = 36.8699°

Acute Angle of Rhombus given Inradius Formula Elements

Variables

Functions

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

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

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 Acute Angle of Rhombus

Go Acute Angle of Rhombus given Long Diagonal

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

Go Acute Angle of Rhombus given Short Diagonal

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

Go Acute Angle of Rhombus given both Diagonals

∠ Acute = a \sin (\frac{2 \cdot d Long \cdot d Short}{{d Long}^{2} + {d Short}^{2}})

Go Acute Angle of Rhombus given Area

∠ Acute = a \sin (\frac{A}{S^{2}})

How to Evaluate Acute Angle of Rhombus given Inradius?

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

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

FAQs on Acute Angle of Rhombus given Inradius

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

The formula of Acute Angle of Rhombus given Inradius is expressed as Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus). Here is an example- 2112.49 = asin((2*3)/10).

How to calculate Acute Angle of Rhombus given Inradius?

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

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

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

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

Can the Acute Angle of Rhombus given Inradius be negative?

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

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

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

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