Diagonal 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%

✖Diagonal of Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle.ⓘ Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals [d]

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Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))
d = 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

Diagonal of Rectangle - (Measured in Meter) - Diagonal of Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle.
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

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

Evaluating ... ...

d = 10.0522106028634

STEP 3: Convert Result to Output's Unit

10.0522106028634 Meter --> No Conversion Required

FINAL ANSWER

10.0522106028634 ≈ 10.05221 Meter <-- Diagonal of Rectangle

(Calculation completed in 00.005 seconds)

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Osmania University (OU), Hyderabad

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< Diagonal of Rectangle Calculators

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

Diagonal of Rectangle given Area and Breadth

LaTeX Go Diagonal of Rectangle = sqrt((Area of Rectangle/Breadth of Rectangle)^2+Breadth of Rectangle^2)

Diagonal of Rectangle given Area and Length

LaTeX Go Diagonal of Rectangle = sqrt((Area of Rectangle/Length of Rectangle)^2+Length of Rectangle^2)

Diagonal of Rectangle

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

Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula

LaTeX Go

Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2))))
d = 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 Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals?

Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals calculator uses Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))) to calculate the Diagonal of Rectangle, The Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the length of the line joining any pair of opposite vertices of the Rectangle and calculated using Perimeter and Obtuse Angle between Diagonals of the Rectangle. Diagonal of Rectangle is denoted by d symbol.

How to calculate Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals using this online calculator? To use this online calculator for Diagonal 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 Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals calculation can be explained with given input values -> 10.05221 = 28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2)))).

FAQ

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

The Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the length of the line joining any pair of opposite vertices of the Rectangle and calculated using Perimeter and Obtuse Angle between Diagonals of the Rectangle and is represented as d = P/2*1/(sqrt(1+sin(2*((pi-∠_d(Obtuse))/2)))) or Diagonal of Rectangle = 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 Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals?

The Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals formula is defined as the length of the line joining any pair of opposite vertices of the Rectangle and calculated using Perimeter and Obtuse Angle between Diagonals of the Rectangle is calculated using Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))). To calculate Diagonal 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 Diagonal of Rectangle?

In this formula, Diagonal 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 -

Diagonal of Rectangle = sqrt((Area of Rectangle/Breadth of Rectangle)^2+Breadth of Rectangle^2)
Diagonal of Rectangle = sqrt((2*Breadth of Rectangle^2)-(Perimeter of Rectangle*Breadth of Rectangle)+(Perimeter of Rectangle^2/4))
Diagonal of Rectangle = sqrt((Area of Rectangle/Length of Rectangle)^2+Length of Rectangle^2)

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