Circumradius of Rectangle given Breadth and Obtuse Angle between Diagonals Calculator

✖Breadth of Rectangle is any one of the pair of parallel sides which are shorter than the remaining pair of parallel sides.ⓘ Breadth of Rectangle [b]			+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 Breadth and Obtuse Angle between Diagonals [r_c]

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Circumradius of Rectangle given Breadth and Obtuse Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi-Obtuse Angle between Diagonals of Rectangle)/2))
r_c = 1/2*(b*cosec((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

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
cosec - The cosecant function is a trigonometric function that is the reciprocal of the sine function., cosec(Angle)

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.
Breadth of Rectangle - (Measured in Meter) - Breadth of Rectangle is any one of the pair of parallel sides which are shorter than the remaining pair of parallel sides.
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

Breadth of Rectangle: 6 Meter --> 6 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*(b*cosec((pi-∠_d(Obtuse))/2)) --> 1/2*(6*cosec((pi-1.9198621771934)/2))

Evaluating ... ...

r_c = 5.23034038686194

STEP 3: Convert Result to Output's Unit

5.23034038686194 Meter --> No Conversion Required

FINAL ANSWER

5.23034038686194 ≈ 5.23034 Meter <-- Circumradius of Rectangle

(Calculation completed in 00.007 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 Breadth and Obtuse Angle between Diagonals Formula

LaTeX Go

Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi-Obtuse Angle between Diagonals of Rectangle)/2))
r_c = 1/2*(b*cosec((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 Breadth and Obtuse Angle between Diagonals?

Circumradius of Rectangle given Breadth and Obtuse Angle between Diagonals calculator uses Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi-Obtuse Angle between Diagonals of Rectangle)/2)) to calculate the Circumradius of Rectangle, The Circumradius of Rectangle given Breadth 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 breadth and obtuse angle between diagonals of the Rectangle. Circumradius of Rectangle is denoted by r_c symbol.

How to calculate Circumradius of Rectangle given Breadth and Obtuse Angle between Diagonals using this online calculator? To use this online calculator for Circumradius of Rectangle given Breadth and Obtuse Angle between Diagonals, enter Breadth of Rectangle (b) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) and hit the calculate button. Here is how the Circumradius of Rectangle given Breadth and Obtuse Angle between Diagonals calculation can be explained with given input values -> 5.23034 = 1/2*(6*cosec((pi-1.9198621771934)/2)).

FAQ

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

The Circumradius of Rectangle given Breadth 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 breadth and obtuse angle between diagonals of the Rectangle and is represented as r_c = 1/2*(b*cosec((pi-∠_d(Obtuse))/2)) or Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi-Obtuse Angle between Diagonals of Rectangle)/2)). Breadth of Rectangle is any one of the pair of parallel sides which are shorter than the remaining pair of parallel sides & 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 Breadth and Obtuse Angle between Diagonals?

The Circumradius of Rectangle given Breadth 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 breadth and obtuse angle between diagonals of the Rectangle is calculated using Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi-Obtuse Angle between Diagonals of Rectangle)/2)). To calculate Circumradius of Rectangle given Breadth and Obtuse Angle between Diagonals, you need Breadth of Rectangle (b) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)). With our tool, you need to enter the respective value for Breadth 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 Breadth 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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