Circumradius of Rectangle given Area and Acute Angle between Diagonals Calculator

✖Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.ⓘ Area of Rectangle [A]			+10% -10%
✖Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.ⓘ Acute Angle between Diagonals of Rectangle [∠_d(Acute)]			+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 Area and Acute Angle between Diagonals [r_c]

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Circumradius of Rectangle given Area and Acute Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumradius of Rectangle = 1/2*(sqrt(Area of Rectangle*cot(Acute Angle between Diagonals of Rectangle/2)))/(cos(Acute Angle between Diagonals of Rectangle/2))
r_c = 1/2*(sqrt(A*cot(∠_d(Acute)/2)))/(cos(∠_d(Acute)/2))
This formula uses 3 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(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.
Area of Rectangle - (Measured in Square Meter) - Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.
Acute Angle between Diagonals of Rectangle - (Measured in Radian) - Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Area of Rectangle: 48 Square Meter --> 48 Square Meter No Conversion Required
Acute Angle between Diagonals of Rectangle: 70 Degree --> 1.2217304763958 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_c = 1/2*(sqrt(A*cot(∠_d(Acute)/2)))/(cos(∠_d(Acute)/2)) --> 1/2*(sqrt(48*cot(1.2217304763958/2)))/(cos(1.2217304763958/2))

Evaluating ... ...

r_c = 5.05373787798932

STEP 3: Convert Result to Output's Unit

5.05373787798932 Meter --> No Conversion Required

FINAL ANSWER

5.05373787798932 ≈ 5.053738 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 Area and Acute Angle between Diagonals Formula

LaTeX Go

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 Area and Acute Angle between Diagonals?

Circumradius of Rectangle given Area and Acute Angle between Diagonals calculator uses Circumradius of Rectangle = 1/2*(sqrt(Area of Rectangle*cot(Acute Angle between Diagonals of Rectangle/2)))/(cos(Acute Angle between Diagonals of Rectangle/2)) to calculate the Circumradius of Rectangle, The Circumradius of Rectangle given Area and Acute 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 area and acute angle between diagonals of the Rectangle. Circumradius of Rectangle is denoted by r_c symbol.

How to calculate Circumradius of Rectangle given Area and Acute Angle between Diagonals using this online calculator? To use this online calculator for Circumradius of Rectangle given Area and Acute Angle between Diagonals, enter Area of Rectangle (A) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)) and hit the calculate button. Here is how the Circumradius of Rectangle given Area and Acute Angle between Diagonals calculation can be explained with given input values -> 5.053738 = 1/2*(sqrt(48*cot(1.2217304763958/2)))/(cos(1.2217304763958/2)).

FAQ

What is Circumradius of Rectangle given Area and Acute Angle between Diagonals?

The Circumradius of Rectangle given Area and Acute 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 area and acute angle between diagonals of the Rectangle and is represented as r_c = 1/2*(sqrt(A*cot(∠_d(Acute)/2)))/(cos(∠_d(Acute)/2)) or Circumradius of Rectangle = 1/2*(sqrt(Area of Rectangle*cot(Acute Angle between Diagonals of Rectangle/2)))/(cos(Acute Angle between Diagonals of Rectangle/2)). Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle & Acute Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is less than 90 degrees.

How to calculate Circumradius of Rectangle given Area and Acute Angle between Diagonals?

The Circumradius of Rectangle given Area and Acute 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 area and acute angle between diagonals of the Rectangle is calculated using Circumradius of Rectangle = 1/2*(sqrt(Area of Rectangle*cot(Acute Angle between Diagonals of Rectangle/2)))/(cos(Acute Angle between Diagonals of Rectangle/2)). To calculate Circumradius of Rectangle given Area and Acute Angle between Diagonals, you need Area of Rectangle (A) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)). With our tool, you need to enter the respective value for Area of Rectangle & Acute 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 Area of Rectangle & Acute 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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