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Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula

GoCircumradius of Rectangle given Perimeter and Length Formula

GoCircumradius of Rectangle Formula

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Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle. Check FAQs

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

r_c - Circumradius of Rectangle?P - Perimeter of Rectangle?∠_d(Obtuse) - Obtuse Angle between Diagonals of Rectangle?π - Archimedes' constant?

Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals Example

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Here is how the Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals equation looks like with Values.

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

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

5.0261 = \frac{1}{2} \cdot (\frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110}{2}))}})

5.0261m = \frac{1}{2} \cdot (\frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110°}{2}))}})

5.0261 = \frac{1}{2} \cdot (\frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110}{2}))}})

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Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r c = 5.02610530143168m

LAST Step Rounding Answer

∴

r c = 5.0261m

Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula Elements

Variables

Constants

Functions

Circumradius of Rectangle

Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius 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 Circumradius of Rectangle

Go Circumradius of Rectangle given Perimeter and Length

r c = \frac{\sqrt{P^{2} - (4 \cdot P \cdot l) + (8 \cdot l^{2})}}{4}

Go Circumradius of Rectangle

r c = \frac{\sqrt{l^{2} + b^{2}}}{2}

Go Circumradius of Rectangle given Perimeter and Breadth

r c = \frac{\sqrt{P^{2} - (4 \cdot P \cdot b) + (8 \cdot b^{2})}}{4}

Go Circumradius of Rectangle given Diagonal

r c = \frac{d}{2}

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

Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals evaluator uses Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))) to evaluate the Circumradius of Rectangle, The Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the radius 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. Circumradius of Rectangle is denoted by r_c symbol.

How to evaluate Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals using this online evaluator? To use this online evaluator for Circumradius 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 Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals

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

The formula of Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals is expressed as Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))). Here is an example- 5.026105 = 1/2*(28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2))))).

How to calculate Circumradius 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 Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals using the formula - Circumradius of Rectangle = 1/2*(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 Circumradius of Rectangle?

Here are the different ways to Calculate Circumradius of Rectangle-

Circumradius of Rectangle=sqrt(Perimeter of Rectangle^2-(4*Perimeter of Rectangle*Length of Rectangle)+(8*Length of Rectangle^2))/4
Circumradius of Rectangle=sqrt(Length of Rectangle^2+Breadth of Rectangle^2)/2
Circumradius of Rectangle=sqrt(Perimeter of Rectangle^2-(4*Perimeter of Rectangle*Breadth of Rectangle)+(8*Breadth of Rectangle^2))/4

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

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

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

Circumradius 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 Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals can be measured.

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