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Central Angle of Annulus Sector given Diagonal Formula

GoCentral Angle of Annulus Sector given Area Formula

GoCentral Angle of Annulus Sector given Outer Arc Length and Breadth Formula

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Central Angle of Annulus Sector is the angle whose apex (vertex) is the center of the concentric circles of Annulus and whose legs (sides) are radii intersecting the circles in four distinct points. Check FAQs

∠ Central(Sector) = a \cos (\frac{{r Outer}^{2} + {r Inner}^{2} - {d Sector}^{2}}{2 \cdot r Outer \cdot r Inner})

∠_{Central(Sector)} - Central Angle of Annulus Sector?r_Outer - Outer Circle Radius of Annulus?r_Inner - Inner Circle Radius of Annulus?d_Sector - Diagonal of Annulus Sector?

Central Angle of Annulus Sector given Diagonal Example

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Here is how the Central Angle of Annulus Sector given Diagonal equation looks like with Values.

Here is how the Central Angle of Annulus Sector given Diagonal equation looks like with Units.

Here is how the Central Angle of Annulus Sector given Diagonal equation looks like.

43.5312 = a \cos (\frac{10^{2} + 6^{2} - 7^{2}}{2 \cdot 10 \cdot 6})

43.5312° = a \cos (\frac{{10m}^{2} + {6m}^{2} - {7m}^{2}}{2 \cdot 10m \cdot 6m})

43.5312 = a \cos (\frac{10^{2} + 6^{2} - 7^{2}}{2 \cdot 10 \cdot 6})

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Central Angle of Annulus Sector given Diagonal Solution

Follow our step by step solution on how to calculate Central Angle of Annulus Sector given Diagonal?

FIRST Step Consider the formula

∠ Central(Sector) = a \cos (\frac{{r Outer}^{2} + {r Inner}^{2} - {d Sector}^{2}}{2 \cdot r Outer \cdot r Inner})

Next Step Substitute values of Variables

∴

∠ Central(Sector) = a \cos (\frac{{10m}^{2} + {6m}^{2} - {7m}^{2}}{2 \cdot 10m \cdot 6m})

Next Step Prepare to Evaluate

∴

∠ Central(Sector) = a \cos (\frac{10^{2} + 6^{2} - 7^{2}}{2 \cdot 10 \cdot 6})

Next Step Evaluate

∴

∠ Central(Sector) = 0.759761932507315rad

Next Step Convert to Output's Unit

∴

∠ Central(Sector) = 43.5311521673806°

LAST Step Rounding Answer

∴

∠ Central(Sector) = 43.5312°

Central Angle of Annulus Sector given Diagonal Formula Elements

Variables

Functions

Central Angle of Annulus Sector

Central Angle of Annulus Sector is the angle whose apex (vertex) is the center of the concentric circles of Annulus and whose legs (sides) are radii intersecting the circles in four distinct points.

Symbol: ∠_{Central(Sector)}

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Central Angle of Annulus Sector

Outer Circle Radius of Annulus

Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary.

Symbol: r_Outer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Circle Radius of Annulus

Inner Circle Radius of Annulus

Inner Circle Radius of Annulus is the radius of its cavity and it is the smaller radius among two concentric circles.

Symbol: r_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Circle Radius of Annulus

Diagonal of Annulus Sector

Diagonal of Annulus Sector is a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc.

Symbol: d_Sector

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Annulus Sector

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other Formulas to find Central Angle of Annulus Sector

Go Central Angle of Annulus Sector given Area

∠ Central(Sector) = \frac{2 \cdot A Sector}{{r Outer}^{2} - {r Inner}^{2}}

Go Central Angle of Annulus Sector given Outer Arc Length and Breadth

∠ Central(Sector) = \frac{l Outer Arc(Sector)}{r Inner + b}

Go Central Angle of Annulus Sector given Inner Arc Length and Breadth

∠ Central(Sector) = \frac{l Inner Arc(Sector)}{r Outer - b}

Go Central Angle of Annulus Sector given Perimeter

∠ Central(Sector) = \frac{P Sector - (2 \cdot (r Outer - r Inner))}{r Outer + r Inner}

How to Evaluate Central Angle of Annulus Sector given Diagonal?

Central Angle of Annulus Sector given Diagonal evaluator uses Central Angle of Annulus Sector = acos((Outer Circle Radius of Annulus^2+Inner Circle Radius of Annulus^2-Diagonal of Annulus Sector^2)/(2*Outer Circle Radius of Annulus*Inner Circle Radius of Annulus)) to evaluate the Central Angle of Annulus Sector, The Central Angle of Annulus Sector given Diagonal formula is defined as the angle whose apex (vertex) is the center of the concentric circles of Annulus and whose legs (sides) are radii intersecting the circles in four distinct points, calculated using diagonal of Annulus Sector. Central Angle of Annulus Sector is denoted by ∠_{Central(Sector)} symbol.

How to evaluate Central Angle of Annulus Sector given Diagonal using this online evaluator? To use this online evaluator for Central Angle of Annulus Sector given Diagonal, enter Outer Circle Radius of Annulus (r_Outer), Inner Circle Radius of Annulus (r_Inner) & Diagonal of Annulus Sector (d_Sector) and hit the calculate button.

FAQs on Central Angle of Annulus Sector given Diagonal

What is the formula to find Central Angle of Annulus Sector given Diagonal?

The formula of Central Angle of Annulus Sector given Diagonal is expressed as Central Angle of Annulus Sector = acos((Outer Circle Radius of Annulus^2+Inner Circle Radius of Annulus^2-Diagonal of Annulus Sector^2)/(2*Outer Circle Radius of Annulus*Inner Circle Radius of Annulus)). Here is an example- 2494.151 = acos((10^2+6^2-7^2)/(2*10*6)).

How to calculate Central Angle of Annulus Sector given Diagonal?

With Outer Circle Radius of Annulus (r_Outer), Inner Circle Radius of Annulus (r_Inner) & Diagonal of Annulus Sector (d_Sector) we can find Central Angle of Annulus Sector given Diagonal using the formula - Central Angle of Annulus Sector = acos((Outer Circle Radius of Annulus^2+Inner Circle Radius of Annulus^2-Diagonal of Annulus Sector^2)/(2*Outer Circle Radius of Annulus*Inner Circle Radius of Annulus)). This formula also uses Cosine, Inverse Cosine function(s).

What are the other ways to Calculate Central Angle of Annulus Sector?

Here are the different ways to Calculate Central Angle of Annulus Sector-

Central Angle of Annulus Sector=(2*Area of Annulus Sector)/(Outer Circle Radius of Annulus^2-Inner Circle Radius of Annulus^2)
Central Angle of Annulus Sector=Outer Arc Length of Annulus Sector/(Inner Circle Radius of Annulus+Breadth of Annulus)
Central Angle of Annulus Sector=Inner Arc Length of Annulus Sector/(Outer Circle Radius of Annulus-Breadth of Annulus)

Can the Central Angle of Annulus Sector given Diagonal be negative?

No, the Central Angle of Annulus Sector given Diagonal, measured in Angle cannot be negative.

Which unit is used to measure Central Angle of Annulus Sector given Diagonal?

Central Angle of Annulus Sector given Diagonal is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Central Angle of Annulus Sector given Diagonal can be measured.

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Central Angle of Annulus Sector given Diagonal Formula

​GoCentral Angle of Annulus Sector given Area Formula

​GoCentral Angle of Annulus Sector given Outer Arc Length and Breadth Formula

Central Angle of Annulus Sector given Diagonal Example

Central Angle of Annulus Sector given Diagonal Solution

Central Angle of Annulus Sector given Diagonal Formula Elements

Other Formulas to find Central Angle of Annulus Sector

How to Evaluate Central Angle of Annulus Sector given Diagonal?

FAQs on Central Angle of Annulus Sector given Diagonal

Variable Name

GoCentral Angle of Annulus Sector given Area Formula

GoCentral Angle of Annulus Sector given Outer Arc Length and Breadth Formula