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Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length 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 ∠ dl)}}

d - Diagonal of Rectangle?P - Perimeter of Rectangle?∠_dl - Angle between Diagonal and Length of Rectangle?

Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length Example

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

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

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

10.0522 = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot 35)}}

10.0522m = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot 35°)}}

10.0522 = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot 35)}}

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Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot 35°)}}

Next Step Convert Units

∴

d = \frac{28m}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot 0.6109rad)}}

Next Step Prepare to Evaluate

∴

d = \frac{28}{2} \cdot \frac{1}{\sqrt{1 + \sin (2 \cdot 0.6109)}}

Next Step Evaluate

∴

d = 10.0522106028639m

LAST Step Rounding Answer

∴

d = 10.0522m

Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length Formula Elements

Variables

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

Angle between Diagonal and Length of Rectangle

Angle between Diagonal and Length of Rectangle is the measure of wideness of the angle made by any diagonal with the length of the Rectangle.

Symbol: ∠_dl

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Angle between Diagonal and Length of Rectangle

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 Angle between Diagonal and Length?

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

How to evaluate Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length using this online evaluator? To use this online evaluator for Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length, enter Perimeter of Rectangle (P) & Angle between Diagonal and Length of Rectangle (∠_dl) and hit the calculate button.

FAQs on Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length

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

The formula of Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length is expressed as Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*Angle between Diagonal and Length of Rectangle))). Here is an example- 10.05221 = 28/2*1/(sqrt(1+sin(2*0.610865238197901))).

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

With Perimeter of Rectangle (P) & Angle between Diagonal and Length of Rectangle (∠_dl) we can find Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length using the formula - Diagonal of Rectangle = Perimeter of Rectangle/2*1/(sqrt(1+sin(2*Angle between Diagonal and Length of Rectangle))). This formula also uses 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 Angle between Diagonal and Length be negative?

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

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

Diagonal of Rectangle given Perimeter and Angle between Diagonal and Length 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 Angle between Diagonal and Length can be measured.

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