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Central Angle of Annulus Sector given Diagonal and Outer Circle Radius 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 (1 - (\frac{{d Sector}^{2} - b^{2}}{2 \cdot r Outer \cdot (r Outer - b)}))

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

Central Angle of Annulus Sector given Diagonal and Outer Circle Radius Example

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Here is how the Central Angle of Annulus Sector given Diagonal and Outer Circle Radius equation looks like.

43.5312 = a \cos (1 - (\frac{7^{2} - 4^{2}}{2 \cdot 10 \cdot (10 - 4)}))

43.5312° = a \cos (1 - (\frac{{7m}^{2} - {4m}^{2}}{2 \cdot 10m \cdot (10m - 4m)}))

43.5312 = a \cos (1 - (\frac{7^{2} - 4^{2}}{2 \cdot 10 \cdot (10 - 4)}))

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Central Angle of Annulus Sector given Diagonal and Outer Circle Radius Solution

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

FIRST Step Consider the formula

∠ Central(Sector) = a \cos (1 - (\frac{{d Sector}^{2} - b^{2}}{2 \cdot r Outer \cdot (r Outer - b)}))

Next Step Substitute values of Variables

∴

∠ Central(Sector) = a \cos (1 - (\frac{{7m}^{2} - {4m}^{2}}{2 \cdot 10m \cdot (10m - 4m)}))

Next Step Prepare to Evaluate

∴

∠ Central(Sector) = a \cos (1 - (\frac{7^{2} - 4^{2}}{2 \cdot 10 \cdot (10 - 4)}))

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 and Outer Circle Radius 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

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

Breadth of Annulus

Breadth of Annulus is defined as the shortest distance or measurement between outer circle and inner circle of Annulus.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Breadth of Annulus

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

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 and Outer Circle Radius?

Central Angle of Annulus Sector given Diagonal and Outer Circle Radius evaluator uses Central Angle of Annulus Sector = acos(1-((Diagonal of Annulus Sector^2-Breadth of Annulus^2)/(2*Outer Circle Radius of Annulus*(Outer Circle Radius of Annulus-Breadth of Annulus)))) to evaluate the Central Angle of Annulus Sector, The Central Angle of Annulus Sector given Diagonal and Outer Circle Radius 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, outer circle radius and breadth of Annulus Sector. Central Angle of Annulus Sector is denoted by ∠_{Central(Sector)} symbol.

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

FAQs on Central Angle of Annulus Sector given Diagonal and Outer Circle Radius

What is the formula to find Central Angle of Annulus Sector given Diagonal and Outer Circle Radius?

The formula of Central Angle of Annulus Sector given Diagonal and Outer Circle Radius is expressed as Central Angle of Annulus Sector = acos(1-((Diagonal of Annulus Sector^2-Breadth of Annulus^2)/(2*Outer Circle Radius of Annulus*(Outer Circle Radius of Annulus-Breadth of Annulus)))). Here is an example- 2494.151 = acos(1-((7^2-4^2)/(2*10*(10-4)))).

How to calculate Central Angle of Annulus Sector given Diagonal and Outer Circle Radius?

With Diagonal of Annulus Sector (d_Sector), Breadth of Annulus (b) & Outer Circle Radius of Annulus (r_Outer) we can find Central Angle of Annulus Sector given Diagonal and Outer Circle Radius using the formula - Central Angle of Annulus Sector = acos(1-((Diagonal of Annulus Sector^2-Breadth of Annulus^2)/(2*Outer Circle Radius of Annulus*(Outer Circle Radius of Annulus-Breadth of Annulus)))). This formula also uses Cosine (cos), Inverse Cosine (acos) 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 and Outer Circle Radius be negative?

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

Which unit is used to measure Central Angle of Annulus Sector given Diagonal and Outer Circle Radius?

Central Angle of Annulus Sector given Diagonal and Outer Circle Radius 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 and Outer Circle Radius can be measured.

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Central Angle of Annulus Sector given Diagonal and Outer Circle Radius 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 and Outer Circle Radius Example

Central Angle of Annulus Sector given Diagonal and Outer Circle Radius Solution

Central Angle of Annulus Sector given Diagonal and Outer Circle Radius Formula Elements

Other Formulas to find Central Angle of Annulus Sector

How to Evaluate Central Angle of Annulus Sector given Diagonal and Outer Circle Radius?

FAQs on Central Angle of Annulus Sector given Diagonal and Outer Circle Radius

Variable Name

GoCentral Angle of Annulus Sector given Area Formula

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