Circumradius of Rectangle given Perimeter and Acute 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*(Acute Angle between Diagonals of Rectangle/2)))))
rc = 1/2*(P/2*1/(sqrt(1+sin(2*(d(Acute)/2)))))
This formula uses 2 Functions, 3 Variables
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.
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
Perimeter of Rectangle: 28 Meter --> 28 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
rc = 1/2*(P/2*1/(sqrt(1+sin(2*(∠d(Acute)/2))))) --> 1/2*(28/2*1/(sqrt(1+sin(2*(1.2217304763958/2)))))
Evaluating ... ...
rc = 5.02610530143194
STEP 3: Convert Result to Output's Unit
5.02610530143194 Meter --> No Conversion Required
FINAL ANSWER
5.02610530143194 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 Acute Angle between Diagonals Formula

​LaTeX ​Go
Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*(Acute Angle between Diagonals of Rectangle/2)))))
rc = 1/2*(P/2*1/(sqrt(1+sin(2*(d(Acute)/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 Acute Angle between Diagonals?

Circumradius of Rectangle given Perimeter and Acute Angle between Diagonals calculator uses Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*(Acute Angle between Diagonals of Rectangle/2))))) to calculate the Circumradius of Rectangle, The Circumradius of Rectangle given Perimeter 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 perimeter and acute angle between diagonals of the Rectangle. Circumradius of Rectangle is denoted by rc symbol.

How to calculate Circumradius of Rectangle given Perimeter and Acute Angle between Diagonals using this online calculator? To use this online calculator for Circumradius of Rectangle given Perimeter and Acute Angle between Diagonals, enter Perimeter of Rectangle (P) & Acute Angle between Diagonals of Rectangle (∠d(Acute)) and hit the calculate button. Here is how the Circumradius of Rectangle given Perimeter and Acute Angle between Diagonals calculation can be explained with given input values -> 5.026105 = 1/2*(28/2*1/(sqrt(1+sin(2*(1.2217304763958/2))))).

FAQ

What is Circumradius of Rectangle given Perimeter and Acute Angle between Diagonals?
The Circumradius of Rectangle given Perimeter 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 perimeter and acute angle between diagonals of the Rectangle and is represented as rc = 1/2*(P/2*1/(sqrt(1+sin(2*(∠d(Acute)/2))))) or Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*(Acute Angle between Diagonals of Rectangle/2))))). Perimeter of Rectangle is the total length of all the boundary lines 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 Perimeter and Acute Angle between Diagonals?
The Circumradius of Rectangle given Perimeter 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 perimeter and acute angle between diagonals of the Rectangle is calculated using Circumradius of Rectangle = 1/2*(Perimeter of Rectangle/2*1/(sqrt(1+sin(2*(Acute Angle between Diagonals of Rectangle/2))))). To calculate Circumradius of Rectangle given Perimeter and Acute Angle between Diagonals, you need Perimeter of Rectangle (P) & Acute Angle between Diagonals of Rectangle (∠d(Acute)). With our tool, you need to enter the respective value for Perimeter 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 Perimeter 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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