Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth 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%
✖Angle between Diagonal and Breadth of Rectangle is the measure of wideness of the angle made by any diagonal with the breadth of the Rectangle.ⓘ Angle between Diagonal and Breadth of Rectangle [∠_db]			+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 Angle between Diagonal and Breadth [r_c]

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Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi/2)-Angle between Diagonal and Breadth of Rectangle))
r_c = 1/2*(b*cosec((pi/2)-∠_db))
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.
Angle between Diagonal and Breadth of Rectangle - (Measured in Radian) - Angle between Diagonal and Breadth of Rectangle is the measure of wideness of the angle made by any diagonal with the breadth of the Rectangle.

STEP 1: Convert Input(s) to Base Unit

Breadth of Rectangle: 6 Meter --> 6 Meter No Conversion Required
Angle between Diagonal and Breadth of Rectangle: 55 Degree --> 0.959931088596701 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = 1/2*(b*cosec((pi/2)-∠_db)) --> 1/2*(6*cosec((pi/2)-0.959931088596701))

Evaluating ... ...

r_c = 5.23034038686195

STEP 3: Convert Result to Output's Unit

5.23034038686195 Meter --> No Conversion Required

FINAL ANSWER

5.23034038686195 ≈ 5.23034 Meter <-- Circumradius of Rectangle

(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad

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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 Angle between Diagonal and Breadth Formula

LaTeX Go

Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi/2)-Angle between Diagonal and Breadth of Rectangle))
r_c = 1/2*(b*cosec((pi/2)-∠_db))

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 Angle between Diagonal and Breadth?

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

How to calculate Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth using this online calculator? To use this online calculator for Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth, enter Breadth of Rectangle (b) & Angle between Diagonal and Breadth of Rectangle (∠_db) and hit the calculate button. Here is how the Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth calculation can be explained with given input values -> 5.23034 = 1/2*(6*cosec((pi/2)-0.959931088596701)).

FAQ

What is Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth?

The Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth 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 angle between diagonal and breadth of the Rectangle and is represented as r_c = 1/2*(b*cosec((pi/2)-∠_db)) or Circumradius of Rectangle = 1/2*(Breadth of Rectangle*cosec((pi/2)-Angle between Diagonal and Breadth of Rectangle)). Breadth of Rectangle is any one of the pair of parallel sides which are shorter than the remaining pair of parallel sides & Angle between Diagonal and Breadth of Rectangle is the measure of wideness of the angle made by any diagonal with the breadth of the Rectangle.

How to calculate Circumradius of Rectangle given Breadth and Angle between Diagonal and Breadth?

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