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Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula

GoDiagonal of Rectangle given Area and Breadth Formula

GoDiagonal of Rectangle given Perimeter and Breadth Formula

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Diagonal of Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle. Check FAQs

d = \frac{P}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{π - ∠ d(Obtuse)}{2}))}}

d - Diagonal of Rectangle?P - Perimeter of Rectangle?∠_d(Obtuse) - Obtuse Angle between Diagonals of Rectangle?π - Archimedes' constant?

Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals Example

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Here is how the Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals equation looks like with Values.

Here is how the Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals equation looks like with Units.

Here is how the Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals equation looks like.

10.0522 = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110}{2}))}}

10.0522m = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110°}{2}))}}

10.0522 = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110}{2}))}}

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Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals Solution

Follow our step by step solution on how to calculate Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals?

FIRST Step Consider the formula

d = \frac{P}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{π - ∠ d(Obtuse)}{2}))}}

Next Step Substitute values of Variables

∴

d = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{π - 110°}{2}))}}

Next Step Substitute values of Constants

∴

d = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 110°}{2}))}}

Next Step Convert Units

∴

d = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 1.9199rad}{2}))}}

Next Step Prepare to Evaluate

∴

d = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot (\frac{3.1416 - 1.9199}{2}))}}

Next Step Evaluate

∴

d = 10.0522106028634m

LAST Step Rounding Answer

∴

d = 10.0522m

Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals Formula Elements

Variables

Constants

Functions

Diagonal of Rectangle

Diagonal of Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Rectangle

Perimeter of Rectangle

Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter of Rectangle

Obtuse Angle between Diagonals of Rectangle

Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

Symbol: ∠_d(Obtuse)

Measurement: AngleUnit: °

Note: Value should be between 90 to 180.

Formulas to find Obtuse Angle between Diagonals of Rectangle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Diagonal of Rectangle

Go Diagonal of Rectangle given Area and Breadth

d = \sqrt{{(\frac{A}{b})}^{2} + b^{2}}

Go Diagonal of Rectangle given Perimeter and Breadth

d = \sqrt{(2 \cdot b^{2}) - (P \cdot b) + (\frac{P^{2}}{4})}

Go Diagonal of Rectangle given Area and Length

d = \sqrt{{(\frac{A}{l})}^{2} + l^{2}}

Go Diagonal of Rectangle

d = \sqrt{l^{2} + b^{2}}

How to Evaluate Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals?

Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals evaluator uses Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))) to evaluate 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 evaluate Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals using this online evaluator? To use this online evaluator 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.

FAQs on Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals

What is the formula to find Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals?

The formula of Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals is expressed as Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))). Here is an example- 10.05221 = 28/2*1/(sqrt(1+sin(2*((pi-1.9198621771934)/2)))).

How to calculate Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals?

With Perimeter of Rectangle (P) & Obtuse Angle between Diagonals of Rectangle (∠_d(Obtuse)) we can find Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals using the formula - Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*((pi-Obtuse Angle between Diagonals of Rectangle)/2)))). This formula also uses Archimedes' constant and , Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Diagonal of Rectangle?

Here are the different ways to Calculate Diagonal of Rectangle-

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)

Can the Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals be negative?

No, the Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals?

Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diagonal of Rectangle given Perimeter and Obtuse Angle between Diagonals can be measured.

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