Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals Calculator

✖Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.ⓘ Perimeter of Rectangle [P]			+10% -10%
✖Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.ⓘ Obtuse Angle between Diagonals of Rectangle [∠_d(Obtuse)]			+10% -10%

✖Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.ⓘ Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals [r_c]

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Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))))
r_c = 1/2*(P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2)))))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., 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., sqrt(Number)

Variables Used

Circumradius of Rectangle - (Measured in Meter) - Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.
Perimeter of Rectangle - (Measured in Meter) - Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.
Obtuse Angle between Diagonals of Rectangle - (Measured in Radian) - Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Rectangle: 28 Meter --> 28 Meter No Conversion Required
Obtuse Angle between Diagonals of Rectangle: 110 Degree --> 1.9198621771934 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = 1/2*(P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2))))) --> 1/2*(28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2)))))

Evaluating ... ...

r_c = 5.02610530143168

STEP 3: Convert Result to Output's Unit

5.02610530143168 Meter --> No Conversion Required

FINAL ANSWER

5.02610530143168 ≈ 5.026105 Meter <-- Circumradius of Rectangle

(Calculation completed in 00.004 seconds)

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< Circumradius of Rectangle Calculators

Circumradius of Rectangle given Perimeter and Breadth

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

Circumradius of Rectangle given Perimeter and Length

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

Circumradius of Rectangle

LaTeX Go Circumradius of Rectangle = sqrt(Length of Rectangle^2+Breadth of Rectangle^2)/2

Circumradius of Rectangle given Diagonal

LaTeX Go Circumradius of Rectangle = Diagonal of Rectangle/2

Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula

LaTeX Go

Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))))
r_c = 1/2*(P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2)))))

What is a Rectangle?

A Rectangle is a two dimensional geometric shape having four sides and four corners. The four sides are in two pairs, in which each pair of lines are equal in length and parallel to each other. And adjacent sides are perpendicular to each other. In general a 2D shape with four boundary edges are called quadrilaterals. So a rectangle is a quadrilateral in which each corner is right angle.

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

Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals calculator uses Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))) to calculate 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 calculate Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals using this online calculator? To use this online calculator 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. Here is how the Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals calculation can be explained with given input values -> 5.026105 = 1/2*(28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2))))).

FAQ

What is Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals?

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 and is represented as r_c = 1/2*(P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2))))) or Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))). Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle & Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

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

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 is calculated using Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))). To calculate Circumradius of Rectangle given Perimeter and Obtuse Angle between Diagonals, you need Perimeter of Rectangle (P) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)). With our tool, you need to enter the respective value for Perimeter of Rectangle & Obtuse Angle between Diagonals of Rectangle 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 Circumradius of Rectangle?

In this formula, Circumradius of Rectangle uses Perimeter of Rectangle & Obtuse Angle between Diagonals of Rectangle. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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