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First Acute Angle of Concave Quadrilateral Calculator

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✖First Outer Side of Concave Quadrilateral is the first outermost side of the Concave Quadrilateral.ⓘ First Outer Side of Concave Quadrilateral [S_{First Outer}]			+10% -10%
✖First Inner Side of Concave Quadrilateral is the first innermost side of the Concave Quadrilateral.ⓘ First Inner Side of Concave Quadrilateral [S_{First Inner}]			+10% -10%
✖Inner Diagonal of Concave Quadrilateral is a straight line joining two opposite corners, and lies inside the region of Concave Quadrilateral.ⓘ Inner Diagonal of Concave Quadrilateral [d_Inner]			+10% -10%

✖The First Acute Angle of Concave Quadrilateral is the angle formed between the first outer and first inner side of the Concave Quadrilateral.ⓘ First Acute Angle of Concave Quadrilateral [∠_{First Acute}]

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First Acute Angle of Concave Quadrilateral Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
∠_{First Acute} = arccos((S_{First Outer}^2+S_{First Inner}^2-d_Inner^2)/(2*S_{First Outer}*S_{First Inner}))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., arccos(Number)

Variables Used

First Acute Angle of Concave Quadrilateral - (Measured in Radian) - The First Acute Angle of Concave Quadrilateral is the angle formed between the first outer and first inner side of the Concave Quadrilateral.
First Outer Side of Concave Quadrilateral - (Measured in Meter) - First Outer Side of Concave Quadrilateral is the first outermost side of the Concave Quadrilateral.
First Inner Side of Concave Quadrilateral - (Measured in Meter) - First Inner Side of Concave Quadrilateral is the first innermost side of the Concave Quadrilateral.
Inner Diagonal of Concave Quadrilateral - (Measured in Meter) - Inner Diagonal of Concave Quadrilateral is a straight line joining two opposite corners, and lies inside the region of Concave Quadrilateral.

STEP 1: Convert Input(s) to Base Unit

First Outer Side of Concave Quadrilateral: 10 Meter --> 10 Meter No Conversion Required
First Inner Side of Concave Quadrilateral: 7 Meter --> 7 Meter No Conversion Required
Inner Diagonal of Concave Quadrilateral: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_{First Acute} = arccos((S_{First Outer}^2+S_{First Inner}^2-d_Inner^2)/(2*S_{First Outer}*S_{First Inner})) --> arccos((10^2+7^2-4^2)/(2*10*7))

Evaluating ... ...

∠_{First Acute} = 0.317560429291522

STEP 3: Convert Result to Output's Unit

0.317560429291522 Radian -->18.1948723387702 Degree (Check conversion here)

FINAL ANSWER

18.1948723387702 ≈ 18.19487 Degree <-- First Acute Angle of Concave Quadrilateral

(Calculation completed in 00.007 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< Concave Quadrilateral Calculators

Inner Diagonal of Concave Quadrilateral

LaTeX Go Inner Diagonal of Concave Quadrilateral = sqrt(Second Outer Side of Concave Quadrilateral^2+Second Inner Side of Concave Quadrilateral^2-(2*Second Outer Side of Concave Quadrilateral*Second Inner Side of Concave Quadrilateral*cos(Third Acute Angle of Concave Quadrilateral)))

Outer Diagonal of Concave Quadrilateral

LaTeX Go Outer Diagonal of Concave Quadrilateral = sqrt(First Outer Side of Concave Quadrilateral^2+Second Outer Side of Concave Quadrilateral^2-(2*First Outer Side of Concave Quadrilateral*Second Outer Side of Concave Quadrilateral*cos(Second Acute Angle of Concave Quadrilateral)))

First Inner Side of Concave Quadrilateral

LaTeX Go First Inner Side of Concave Quadrilateral = sqrt(First Outer Side of Concave Quadrilateral^2+Outer Diagonal of Concave Quadrilateral^2-(2*First Outer Side of Concave Quadrilateral*Outer Diagonal of Concave Quadrilateral*cos(Second Acute Angle of Concave Quadrilateral)))

First Acute Angle of Concave Quadrilateral

LaTeX Go 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))

First Acute Angle of Concave Quadrilateral Formula

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What is a Concave Quadrilateral?

A Concave quadrilateral is defined as, a four-sided polygon with one of its angles greater than 180°, and its diagonals partially outside the bounds of the polygon. The most common example of a concave quadrilateral is the dart.

How to Calculate First Acute Angle of Concave Quadrilateral?

First Acute Angle of Concave Quadrilateral calculator 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 calculate 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 calculate First Acute Angle of Concave Quadrilateral using this online calculator? To use this online calculator 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. Here is how the First Acute Angle of Concave Quadrilateral calculation can be explained with given input values -> 1042.489 = arccos((10^2+7^2-4^2)/(2*10*7)).

FAQ

What is 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 and is represented as ∠_{First Acute} = arccos((S_{First Outer}^2+S_{First Inner}^2-d_Inner^2)/(2*S_{First Outer}*S_{First Inner})) or 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)). First Outer Side of Concave Quadrilateral is the first outermost side of the Concave Quadrilateral, First Inner Side of Concave Quadrilateral is the first innermost side of the Concave Quadrilateral & Inner Diagonal of Concave Quadrilateral is a straight line joining two opposite corners, and lies inside the region of Concave Quadrilateral.

How to calculate 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 is calculated using 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 calculate First Acute Angle of Concave Quadrilateral, you need 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). With our tool, you need to enter the respective value for First Outer Side of Concave Quadrilateral, First Inner Side of Concave Quadrilateral & Inner Diagonal of Concave Quadrilateral and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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