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First Acute Angle of Concave Quadrilateral Formula

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The First Acute Angle of Concave Quadrilateral is the angle formed between the first outer and first inner side of the Concave Quadrilateral. Check FAQs

∠ First Acute = \arccos (\frac{{S First Outer}^{2} + {S First Inner}^{2} - {d Inner}^{2}}{2 \cdot S First Outer \cdot S First Inner})

∠_{First Acute} - First Acute Angle of Concave Quadrilateral?S_{First Outer} - First Outer Side of Concave Quadrilateral?S_{First Inner} - First Inner Side of Concave Quadrilateral?d_Inner - Inner Diagonal of Concave Quadrilateral?

First Acute Angle of Concave Quadrilateral Example

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Here is how the First Acute Angle of Concave Quadrilateral equation looks like with Values.

Here is how the First Acute Angle of Concave Quadrilateral equation looks like with Units.

Here is how the First Acute Angle of Concave Quadrilateral equation looks like.

18.1949 = \arccos (\frac{10^{2} + 7^{2} - 4^{2}}{2 \cdot 10 \cdot 7})

18.1949° = \arccos (\frac{{10m}^{2} + {7m}^{2} - {4m}^{2}}{2 \cdot 10m \cdot 7m})

18.1949 = \arccos (\frac{10^{2} + 7^{2} - 4^{2}}{2 \cdot 10 \cdot 7})

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First Acute Angle of Concave Quadrilateral Solution

Follow our step by step solution on how to calculate First Acute Angle of Concave Quadrilateral?

FIRST Step Consider the formula

∠ First Acute = \arccos (\frac{{S First Outer}^{2} + {S First Inner}^{2} - {d Inner}^{2}}{2 \cdot S First Outer \cdot S First Inner})

Next Step Substitute values of Variables

∴

∠ First Acute = \arccos (\frac{{10m}^{2} + {7m}^{2} - {4m}^{2}}{2 \cdot 10m \cdot 7m})

Next Step Prepare to Evaluate

∴

∠ First Acute = \arccos (\frac{10^{2} + 7^{2} - 4^{2}}{2 \cdot 10 \cdot 7})

Next Step Evaluate

∴

∠ First Acute = 0.317560429291522rad

Next Step Convert to Output's Unit

∴

∠ First Acute = 18.1948723387702°

LAST Step Rounding Answer

∴

∠ First Acute = 18.1949°

First Acute Angle of Concave Quadrilateral Formula Elements

Variables

Functions

First Acute Angle of Concave Quadrilateral

The First Acute Angle of Concave Quadrilateral is the angle formed between the first outer and first inner side of the Concave Quadrilateral.

Symbol: ∠_{First Acute}

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find First Acute Angle of Concave Quadrilateral

First Outer Side of Concave Quadrilateral

First Outer Side of Concave Quadrilateral is the first outermost side of the Concave Quadrilateral.

Symbol: S_{First Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find First Outer Side of Concave Quadrilateral

First Inner Side of Concave Quadrilateral

First Inner Side of Concave Quadrilateral is the first innermost side of the Concave Quadrilateral.

Symbol: S_{First Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find First Inner Side of Concave Quadrilateral

Inner Diagonal of Concave Quadrilateral

Inner Diagonal of Concave Quadrilateral is a straight line joining two opposite corners, and lies inside the region of Concave Quadrilateral.

Symbol: d_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Diagonal of Concave 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 Concave Quadrilateral category

Go Outer Diagonal of Concave Quadrilateral

d Outer = \sqrt{{S First Outer}^{2} + {S Second Outer}^{2} - (2 \cdot S First Outer \cdot S Second Outer \cdot \cos (∠ Second Acute))}

Go Inner Diagonal of Concave Quadrilateral

d Inner = \sqrt{{S Second Outer}^{2} + {S Second Inner}^{2} - (2 \cdot S Second Outer \cdot S Second Inner \cdot \cos (∠ Third Acute))}

Go First Inner Side of Concave Quadrilateral

S First Inner = \sqrt{{S First Outer}^{2} + {d Outer}^{2} - (2 \cdot S First Outer \cdot d Outer \cdot \cos (∠ Second Acute))}

Go Reflex Angle of Concave Quadrilateral

∠ Reflex = (2 \cdot π) - (∠ First Acute + ∠ Third Acute + ∠ Second Acute)

How to Evaluate First Acute Angle of Concave Quadrilateral?

First Acute Angle of Concave Quadrilateral evaluator uses First Acute Angle of Concave Quadrilateral = arccos((First Outer Side of Concave Quadrilateral^2+First Inner Side of Concave Quadrilateral^2-Inner Diagonal of Concave Quadrilateral^2)/(2*First Outer Side of Concave Quadrilateral*First Inner Side of Concave Quadrilateral)) to evaluate the First Acute Angle of Concave Quadrilateral, First Acute angle of Concave Quadrilateral formula is defined as the acute angle formed due to the intersection of first outer and first inner side of Concave quadrilateral. First Acute Angle of Concave Quadrilateral is denoted by ∠_{First Acute} symbol.

How to evaluate First Acute Angle of Concave Quadrilateral using this online evaluator? To use this online evaluator for First Acute Angle of Concave Quadrilateral, enter First Outer Side of Concave Quadrilateral (S_{First Outer}), First Inner Side of Concave Quadrilateral (S_{First Inner}) & Inner Diagonal of Concave Quadrilateral (d_Inner) and hit the calculate button.

FAQs on First Acute Angle of Concave Quadrilateral

What is the formula to find First Acute Angle of Concave Quadrilateral?

The formula of First Acute Angle of Concave Quadrilateral is expressed as First Acute Angle of Concave Quadrilateral = arccos((First Outer Side of Concave Quadrilateral^2+First Inner Side of Concave Quadrilateral^2-Inner Diagonal of Concave Quadrilateral^2)/(2*First Outer Side of Concave Quadrilateral*First Inner Side of Concave Quadrilateral)). Here is an example- 1042.489 = arccos((10^2+7^2-4^2)/(2*10*7)).

How to calculate First Acute Angle of Concave Quadrilateral?

With First Outer Side of Concave Quadrilateral (S_{First Outer}), First Inner Side of Concave Quadrilateral (S_{First Inner}) & Inner Diagonal of Concave Quadrilateral (d_Inner) we can find First Acute Angle of Concave Quadrilateral using the formula - First Acute Angle of Concave Quadrilateral = arccos((First Outer Side of Concave Quadrilateral^2+First Inner Side of Concave Quadrilateral^2-Inner Diagonal of Concave Quadrilateral^2)/(2*First Outer Side of Concave Quadrilateral*First Inner Side of Concave Quadrilateral)). This formula also uses Cosine (cos), Inverse Cosine (arccos) function(s).

Can the First Acute Angle of Concave Quadrilateral be negative?

No, the First Acute Angle of Concave Quadrilateral, measured in Angle cannot be negative.

Which unit is used to measure First Acute Angle of Concave Quadrilateral?

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

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First Acute Angle of Concave Quadrilateral Formula

First Acute Angle of Concave Quadrilateral Example

First Acute Angle of Concave Quadrilateral Solution

First Acute Angle of Concave Quadrilateral Formula Elements

Other formulas in Concave Quadrilateral category

How to Evaluate First Acute Angle of Concave Quadrilateral?

FAQs on First Acute Angle of Concave Quadrilateral

Variable Name