First Inner Side 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%
✖Outer Diagonal of Concave Quadrilateral is a straight line joining two opposite corners, and lies outside the region of the Concave Quadrilateral.ⓘ Outer Diagonal of Concave Quadrilateral [d_Outer]			+10% -10%
✖Second Acute Angle of Concave Quadrilateral is the angle formed between second outer and second inner side of the Concave Quadrilateral.ⓘ Second Acute Angle of Concave Quadrilateral [∠_{Second Acute}]			+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}]

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Formula

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First Inner Side of Concave Quadrilateral

Formula

`"S"_{"First Inner"} = sqrt("S"_{"First Outer"}^2+"d"_{"Outer"}^2-(2*"S"_{"First Outer"}*"d"_{"Outer"}*cos("∠"_{"Second Acute"})))`

Example

`"7.131824m"=sqrt(("10m")^2+("8m")^2-(2*"10m"*"8m"*cos("45°")))`

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First Inner Side of Concave Quadrilateral Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
S_{First Inner} = sqrt(S_{First Outer}^2+d_Outer^2-(2*S_{First Outer}*d_Outer*cos(∠_{Second Acute})))
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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

First Outer Side of Concave Quadrilateral: 10 Meter --> 10 Meter No Conversion Required
Outer Diagonal of Concave Quadrilateral: 8 Meter --> 8 Meter No Conversion Required
Second Acute Angle of Concave Quadrilateral: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_{First Inner} = sqrt(S_{First Outer}^2+d_Outer^2-(2*S_{First Outer}*d_Outer*cos(∠_{Second Acute}))) --> sqrt(10^2+8^2-(2*10*8*cos(0.785398163397301)))

Evaluating ... ...

S_{First Inner} = 7.13182410117746

STEP 3: Convert Result to Output's Unit

7.13182410117746 Meter --> No Conversion Required

FINAL ANSWER

7.13182410117746 ≈ 7.131824 Meter <-- First Inner Side of Concave Quadrilateral

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Walchand College of Engineering (WCE), Sangli

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< 7 Concave Quadrilateral Calculators

Area of Concave Quadrilateral

Go Area of Concave Quadrilateral = sqrt(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Outer Side of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Inner Side of Concave Quadrilateral))+sqrt(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Outer Side of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Inner Side of Concave Quadrilateral))

Inner Diagonal of Concave Quadrilateral

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

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

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

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))

Perimeter of Concave Quadrilateral

Go Perimeter of Concave Quadrilateral = First Outer Side of Concave Quadrilateral+Second Outer Side of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral+First Inner Side of Concave Quadrilateral

Reflex Angle of Concave Quadrilateral

Go Reflex Angle of Concave Quadrilateral = (2*pi)-(First Acute Angle of Concave Quadrilateral+Third Acute Angle of Concave Quadrilateral+Second Acute Angle of Concave Quadrilateral)

First Inner Side of Concave Quadrilateral Formula

What is a Concave Quadrilateral?

A Quadrilateral is called a concave quadrilateral, if at least one line segment joining the vertices is not a part of the same region of the quadrilateral. That is, any line segment that joins two interior points goes outside the figure.

How to Calculate First Inner Side of Concave Quadrilateral?

First Inner Side of Concave Quadrilateral calculator uses 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))) to calculate the First Inner Side of Concave Quadrilateral, First Inner side of Concave Quadrilateral formula is defined as the length of one of the inner sides of the Concave Quadrilateral. First Inner Side of Concave Quadrilateral is denoted by S_{First Inner} symbol.

How to calculate First Inner Side of Concave Quadrilateral using this online calculator? To use this online calculator for First Inner Side of Concave Quadrilateral, enter First Outer Side of Concave Quadrilateral (S_{First Outer}), Outer Diagonal of Concave Quadrilateral (d_Outer) & Second Acute Angle of Concave Quadrilateral (∠_{Second Acute}) and hit the calculate button. Here is how the First Inner Side of Concave Quadrilateral calculation can be explained with given input values -> 7.131824 = sqrt(10^2+8^2-(2*10*8*cos(0.785398163397301))).

FAQ

What is First Inner Side of Concave Quadrilateral?

First Inner side of Concave Quadrilateral formula is defined as the length of one of the inner sides of the Concave Quadrilateral and is represented as S_{First Inner} = sqrt(S_{First Outer}^2+d_Outer^2-(2*S_{First Outer}*d_Outer*cos(∠_{Second Acute}))) or 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 Outer Side of Concave Quadrilateral is the first outermost side of the Concave Quadrilateral, Outer Diagonal of Concave Quadrilateral is a straight line joining two opposite corners, and lies outside the region of the Concave Quadrilateral & Second Acute Angle of Concave Quadrilateral is the angle formed between second outer and second inner side of the Concave Quadrilateral.

How to calculate First Inner Side of Concave Quadrilateral?

First Inner side of Concave Quadrilateral formula is defined as the length of one of the inner sides of the Concave Quadrilateral is calculated using 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))). To calculate First Inner Side of Concave Quadrilateral, you need First Outer Side of Concave Quadrilateral (S_{First Outer}), Outer Diagonal of Concave Quadrilateral (d_Outer) & Second Acute Angle of Concave Quadrilateral (∠_{Second Acute}). With our tool, you need to enter the respective value for First Outer Side of Concave Quadrilateral, Outer Diagonal of Concave Quadrilateral & Second Acute Angle 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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