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Angle A of Cyclic Quadrilateral Formula

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Angle A of Cyclic Quadrilateral is the space between two adjacent sides of the Cyclic Quadrilateral, forming angle A. Check FAQs

∠A = \arccos (\frac{{S a}^{2} + {S d}^{2} - {S b}^{2} - {S c}^{2}}{2 \cdot ((S a \cdot S d) + (S b \cdot S c))})

∠A - Angle A of Cyclic Quadrilateral?S_a - Side A of Cyclic Quadrilateral?S_d - Side D of Cyclic Quadrilateral?S_b - Side B of Cyclic Quadrilateral?S_c - Side C of Cyclic Quadrilateral?

Angle A of Cyclic Quadrilateral Example

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Here is how the Angle A of Cyclic Quadrilateral equation looks like with Values.

Here is how the Angle A of Cyclic Quadrilateral equation looks like with Units.

Here is how the Angle A of Cyclic Quadrilateral equation looks like.

94.7017 = \arccos (\frac{10^{2} + 5^{2} - 9^{2} - 8^{2}}{2 \cdot ((10 \cdot 5) + (9 \cdot 8))})

94.7017° = \arccos (\frac{{10m}^{2} + {5m}^{2} - {9m}^{2} - {8m}^{2}}{2 \cdot ((10m \cdot 5m) + (9m \cdot 8m))})

94.7017 = \arccos (\frac{10^{2} + 5^{2} - 9^{2} - 8^{2}}{2 \cdot ((10 \cdot 5) + (9 \cdot 8))})

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Angle A of Cyclic Quadrilateral Solution

Follow our step by step solution on how to calculate Angle A of Cyclic Quadrilateral?

FIRST Step Consider the formula

∠A = \arccos (\frac{{S a}^{2} + {S d}^{2} - {S b}^{2} - {S c}^{2}}{2 \cdot ((S a \cdot S d) + (S b \cdot S c))})

Next Step Substitute values of Variables

∴

∠A = \arccos (\frac{{10m}^{2} + {5m}^{2} - {9m}^{2} - {8m}^{2}}{2 \cdot ((10m \cdot 5m) + (9m \cdot 8m))})

Next Step Prepare to Evaluate

∴

∠A = \arccos (\frac{10^{2} + 5^{2} - 9^{2} - 8^{2}}{2 \cdot ((10 \cdot 5) + (9 \cdot 8))})

Next Step Evaluate

∴

∠A = 1.65285560300519rad

Next Step Convert to Output's Unit

∴

∠A = 94.7016501967657°

LAST Step Rounding Answer

∴

∠A = 94.7017°

Angle A of Cyclic Quadrilateral Formula Elements

Variables

Functions

Angle A of Cyclic Quadrilateral

Angle A of Cyclic Quadrilateral is the space between two adjacent sides of the Cyclic Quadrilateral, forming angle A.

Symbol: ∠A

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Angle A of Cyclic Quadrilateral

Side A of Cyclic Quadrilateral

Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side A of Cyclic Quadrilateral

Side D of Cyclic Quadrilateral

Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side D of Cyclic Quadrilateral

Side B of Cyclic Quadrilateral

Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

Symbol: S_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side B of Cyclic Quadrilateral

Side C of Cyclic Quadrilateral

Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.

Symbol: S_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Side C of Cyclic Quadrilateral

cos

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

Syntax: cos(Angle)

arccos

Arccosine 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: arccos(Number)

Other formulas in Angle of Cyclic Quadrilateral category

Go Angle B of Cyclic Quadrilateral

∠B = π - ∠D

Go Angle between Diagonals of Cyclic Quadrilateral

∠ Diagonals = 2 \cdot \arctan (\sqrt{\frac{(s - S b) \cdot (s - S d)}{(s - S a) \cdot (s - S c)}})

Go Angle C of Cyclic Quadrilateral

∠C = π - ∠A

Go Angle D of Cyclic Quadrilateral

∠D = \arccos (\frac{{S d}^{2} + {S c}^{2} - {S a}^{2} - {S b}^{2}}{2 \cdot ((S d \cdot S c) + (S b \cdot S a))})

How to Evaluate Angle A of Cyclic Quadrilateral?

Angle A of Cyclic Quadrilateral evaluator uses Angle A of Cyclic Quadrilateral = arccos((Side A of Cyclic Quadrilateral^2+Side D of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2-Side C of Cyclic Quadrilateral^2)/(2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))) to evaluate the Angle A of Cyclic Quadrilateral, The Angle A of Cyclic Quadrilateral formula is defined as the space between the adjacent sides (A and D) of the Cyclic Quadrilateral, forming angle A. Angle A of Cyclic Quadrilateral is denoted by ∠A symbol.

How to evaluate Angle A of Cyclic Quadrilateral using this online evaluator? To use this online evaluator for Angle A of Cyclic Quadrilateral, enter Side A of Cyclic Quadrilateral (S_a), Side D of Cyclic Quadrilateral (S_d), Side B of Cyclic Quadrilateral (S_b) & Side C of Cyclic Quadrilateral (S_c) and hit the calculate button.

FAQs on Angle A of Cyclic Quadrilateral

What is the formula to find Angle A of Cyclic Quadrilateral?

The formula of Angle A of Cyclic Quadrilateral is expressed as Angle A of Cyclic Quadrilateral = arccos((Side A of Cyclic Quadrilateral^2+Side D of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2-Side C of Cyclic Quadrilateral^2)/(2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))). Here is an example- 5426.005 = arccos((10^2+5^2-9^2-8^2)/(2*((10*5)+(9*8)))).

How to calculate Angle A of Cyclic Quadrilateral?

With Side A of Cyclic Quadrilateral (S_a), Side D of Cyclic Quadrilateral (S_d), Side B of Cyclic Quadrilateral (S_b) & Side C of Cyclic Quadrilateral (S_c) we can find Angle A of Cyclic Quadrilateral using the formula - Angle A of Cyclic Quadrilateral = arccos((Side A of Cyclic Quadrilateral^2+Side D of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2-Side C of Cyclic Quadrilateral^2)/(2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)))). This formula also uses Cosine (cos), Inverse Cosine (arccos) function(s).

Can the Angle A of Cyclic Quadrilateral be negative?

No, the Angle A of Cyclic Quadrilateral, measured in Angle cannot be negative.

Which unit is used to measure Angle A of Cyclic Quadrilateral?

Angle A of Cyclic Quadrilateral is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle A of Cyclic Quadrilateral can be measured.

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Angle A of Cyclic Quadrilateral Formula

Angle A of Cyclic Quadrilateral Example

Angle A of Cyclic Quadrilateral Solution

Angle A of Cyclic Quadrilateral Formula Elements

Other formulas in Angle of Cyclic Quadrilateral category

How to Evaluate Angle A of Cyclic Quadrilateral?

FAQs on Angle A of Cyclic Quadrilateral

Variable Name