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Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula

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Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle. Check FAQs

D c = \frac{P}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{π - ∠ d(Obtuse)}{2}))}}

D_c - Diameter of Circumcircle of Rectangle?P - Perimeter of Rectangle?∠_d(Obtuse) - Obtuse Angle between Diagonals of Rectangle?π - Archimedes' constant?

Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals Example

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Here is how the Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals equation looks like with Units.

Here is how the Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals equation looks like.

10.0522 = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110}{2}))}}

10.0522m = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110°}{2}))}}

10.0522 = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110}{2}))}}

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Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals Solution

Follow our step by step solution on how to calculate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

FIRST Step Consider the formula

D c = \frac{P}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{π - ∠ d(Obtuse)}{2}))}}

Next Step Substitute values of Variables

∴

D c = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{π - 110°}{2}))}}

Next Step Substitute values of Constants

∴

D c = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110°}{2}))}}

Next Step Convert Units

∴

D c = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 1.9199rad}{2}))}}

Next Step Prepare to Evaluate

∴

D c = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 1.9199}{2}))}}

Next Step Evaluate

∴

D c = 10.0522106028634m

LAST Step Rounding Answer

∴

D c = 10.0522m

Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula Elements

Variables

Constants

Functions

Diameter of Circumcircle of Rectangle

Diameter of Circumcircle of Rectangle is the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.

Symbol: D_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Circumcircle of Rectangle

Perimeter of Rectangle

Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter of Rectangle

Obtuse Angle between Diagonals of Rectangle

Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

Symbol: ∠_d(Obtuse)

Measurement: AngleUnit: °

Note: Value should be between 90 to 180.

Formulas to find Obtuse Angle between Diagonals of Rectangle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(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.

Syntax: sqrt(Number)

Other Formulas to find Diameter of Circumcircle of Rectangle

Go Diameter of Circumcircle of Rectangle

D c = \sqrt{l^{2} + b^{2}}

Go Diameter of Circumcircle of Rectangle given Circumradius

D c = 2 \cdot r c

Go Diameter of Circumcircle of Rectangle given Area and Length

D c = \sqrt{{(\frac{A}{l})}^{2} + l^{2}}

Go Diameter of Circumcircle of Rectangle given Area and Breadth

D c = \sqrt{{(\frac{A}{b})}^{2} + b^{2}}

How to Evaluate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals evaluator uses Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))) to evaluate the Diameter of Circumcircle of Rectangle, The Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the diameter of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle, and calculated using perimeter and obtuse angle between diagonals of the Rectangle. Diameter of Circumcircle of Rectangle is denoted by D_c symbol.

How to evaluate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals using this online evaluator? To use this online evaluator for Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals, enter Perimeter of Rectangle (P) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) and hit the calculate button.

FAQs on Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals

What is the formula to find Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

The formula of Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals is expressed as Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))). Here is an example- 10.05221 = 28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2)))).

How to calculate Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

With Perimeter of Rectangle (P) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) we can find Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals using the formula - Diameter of Circumcircle of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Diameter of Circumcircle of Rectangle?

Here are the different ways to Calculate Diameter of Circumcircle of Rectangle-

Diameter of Circumcircle of Rectangle=sqrt(Length of Rectangle^2+Breadth of Rectangle^2)
Diameter of Circumcircle of Rectangle=2*Circumradius of Rectangle
Diameter of Circumcircle of Rectangle=sqrt((Area of Rectangle/Length of Rectangle)^2+Length of Rectangle^2)

Can the Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals be negative?

No, the Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals, measured in Length cannot be negative.

Which unit is used to measure Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals?

Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diameter of Circumcircle of Rectangle given Perimeter and Obtuse Angle between Diagonals can be measured.

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