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Outer diagonal of Concave Quadrilateral Solution

STEP 0: Pre-Calculation Summary
Formula Used
diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B))
d = sqrt((Sa^2)+(Sb^2)-(2*Sa*Sb)*cos(∠B))
This formula uses 2 Functions, 3 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Side A - Side A is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Side B - Side B is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Angle B - The angle B the space between two intersecting lines or surfaces at or close to the point where they meet. (Measured in Degree)
STEP 1: Convert Input(s) to Base Unit
Side A: 8 Meter --> 8 Meter No Conversion Required
Side B: 7 Meter --> 7 Meter No Conversion Required
Angle B: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = sqrt((Sa^2)+(Sb^2)-(2*Sa*Sb)*cos(∠B)) --> sqrt((8^2)+(7^2)-(2*8*7)*cos(0.785398163397301))
Evaluating ... ...
d = 5.81412422528922
STEP 3: Convert Result to Output's Unit
5.81412422528922 Meter --> No Conversion Required
FINAL ANSWER
5.81412422528922 Meter <-- Diagonal
(Calculation completed in 00.016 seconds)

7 Concave Quadrilateral Calculators

Area of Concave Quadrilateral
area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c))) Go
Outer diagonal of Concave Quadrilateral
diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B)) Go
Inner diagonal of Concave Quadrilateral
diagonal = sqrt((Side B^2)+(Side C^2)-(2*Side B*Side C)*cos(Angle C)) Go
Inner side of Concave Quadrilateral
side_d = sqrt(Side A^2+Diagonal^2-(2*Side A*Diagonal)*cos(Angle B)) Go
Acute angle of Concave Quadrilateral
angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D)) Go
Reflex angle of Concave Quadrilateral
angle = (2*pi)-Angle A-Angle B-Angle C Go
Perimeter of concave quadrilateral
perimeter = Side A+Side B+Side C+Side D Go

Outer diagonal of Concave Quadrilateral Formula

diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B))
d = sqrt((Sa^2)+(Sb^2)-(2*Sa*Sb)*cos(∠B))

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 Outer diagonal of Concave Quadrilateral?

Outer diagonal of Concave Quadrilateral calculator uses diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B)) to calculate the Diagonal, The Outer diagonal of Concave Quadrilateral formula is defined as e = √ a² + b² - 2ab * cos( β ) where a, b is outer sides and e is outer diagonal of concave quadrilateral. Diagonal and is denoted by d symbol.

How to calculate Outer diagonal of Concave Quadrilateral using this online calculator? To use this online calculator for Outer diagonal of Concave Quadrilateral, enter Side A (Sa), Side B (Sb) & Angle B (∠B) and hit the calculate button. Here is how the Outer diagonal of Concave Quadrilateral calculation can be explained with given input values -> 5.814124 = sqrt((8^2)+(7^2)-(2*8*7)*cos(0.785398163397301)).

FAQ

What is Outer diagonal of Concave Quadrilateral?
The Outer diagonal of Concave Quadrilateral formula is defined as e = √ a² + b² - 2ab * cos( β ) where a, b is outer sides and e is outer diagonal of concave quadrilateral and is represented as d = sqrt((Sa^2)+(Sb^2)-(2*Sa*Sb)*cos(∠B)) or diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B)). Side A is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, Side B is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back & The angle B the space between two intersecting lines or surfaces at or close to the point where they meet.
How to calculate Outer diagonal of Concave Quadrilateral?
The Outer diagonal of Concave Quadrilateral formula is defined as e = √ a² + b² - 2ab * cos( β ) where a, b is outer sides and e is outer diagonal of concave quadrilateral is calculated using diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B)). To calculate Outer diagonal of Concave Quadrilateral, you need Side A (Sa), Side B (Sb) & Angle B (∠B). With our tool, you need to enter the respective value for Side A, Side B & Angle B and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Diagonal?
In this formula, Diagonal uses Side A, Side B & Angle B. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • diagonal = sqrt((Side A^2)+(Side B^2)-(2*Side A*Side B)*cos(Angle B))
  • diagonal = sqrt((Side B^2)+(Side C^2)-(2*Side B*Side C)*cos(Angle C))
  • side_d = sqrt(Side A^2+Diagonal^2-(2*Side A*Diagonal)*cos(Angle B))
  • angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D))
  • angle = (2*pi)-Angle A-Angle B-Angle C
  • perimeter = Side A+Side B+Side C+Side D
  • area = sqrt(((Outer side a+Inner Diagonal+Inner side d)/2)*((Outer side a+Inner Diagonal+Inner side d)/(2-Outer side a))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner Diagonal))*((Outer side a+Inner Diagonal+Inner side d)/(2-Inner side d)))+ sqrt(((Outer side b+Inner Diagonal+Inner side c)/2)*((Side B+Diagonal+Side C)/(2-Side B))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner Diagonal))*((Outer side b+Inner Diagonal+Inner side c)/(2-Inner side c)))
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