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Acute angle of Concave Quadrilateral Solution

STEP 0: Pre-Calculation Summary
Formula Used
angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D))
∠A = arccos((Sa^2+Sd^2-d^2)/(2*Sa*Sd))
This formula uses 2 Functions, 3 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
arccos - Inverse trigonometric cosine function, arccos(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 D - Side D is a straight line bounding a geometric figure. (Measured in Meter)
Diagonal - A diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Side A: 8 Meter --> 8 Meter No Conversion Required
Side D: 5 Meter --> 5 Meter No Conversion Required
Diagonal: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
∠A = arccos((Sa^2+Sd^2-d^2)/(2*Sa*Sd)) --> arccos((8^2+5^2-8^2)/(2*8*5))
Evaluating ... ...
∠A = 1.25297262286702
STEP 3: Convert Result to Output's Unit
1.25297262286702 Radian -->71.7900431357305 Degree (Check conversion here)
FINAL ANSWER
71.7900431357305 Degree <-- Angle A
(Calculation completed in 00.015 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

Acute angle of Concave Quadrilateral Formula

angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D))
∠A = arccos((Sa^2+Sd^2-d^2)/(2*Sa*Sd))

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 Acute angle of Concave Quadrilateral?

Acute angle of Concave Quadrilateral calculator uses angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D)) to calculate the Angle A, Acute angle of Concave Quadrilateral formula is defined as α = arccos( (a² + d² - f²) / 2ad ) where a is outer side, d is inner side, f is diagonal of concave quadrilateral. Angle A and is denoted by ∠A symbol.

How to calculate Acute angle of Concave Quadrilateral using this online calculator? To use this online calculator for Acute angle of Concave Quadrilateral, enter Side A (Sa), Side D (Sd) & Diagonal (d) and hit the calculate button. Here is how the Acute angle of Concave Quadrilateral calculation can be explained with given input values -> 71.79004 = arccos((8^2+5^2-8^2)/(2*8*5)).

FAQ

What is Acute angle of Concave Quadrilateral?
Acute angle of Concave Quadrilateral formula is defined as α = arccos( (a² + d² - f²) / 2ad ) where a is outer side, d is inner side, f is diagonal of concave quadrilateral and is represented as ∠A = arccos((Sa^2+Sd^2-d^2)/(2*Sa*Sd)) or angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D)). 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 D is a straight line bounding a geometric figure & A diagonal is a straight line joining two opposite corners of a square, rectangle, or another straight-sided shape.
How to calculate Acute angle of Concave Quadrilateral?
Acute angle of Concave Quadrilateral formula is defined as α = arccos( (a² + d² - f²) / 2ad ) where a is outer side, d is inner side, f is diagonal of concave quadrilateral is calculated using angle_a = arccos((Side A^2+Side D^2-Diagonal^2)/(2*Side A*Side D)). To calculate Acute angle of Concave Quadrilateral, you need Side A (Sa), Side D (Sd) & Diagonal (d). With our tool, you need to enter the respective value for Side A, Side D & Diagonal 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 Angle A?
In this formula, Angle A uses Side A, Side D & Diagonal. 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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