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Diagonal of Rectangle given Area and Angle between Diagonal and Breadth Formula

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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{\sqrt{A \cdot \cot ((\frac{π}{2}) - ∠ db)}}{\cos ((\frac{π}{2}) - ∠ db)}

d - Diagonal of Rectangle?A - Area of Rectangle?∠_db - Angle between Diagonal and Breadth of Rectangle?π - Archimedes' constant?

Diagonal of Rectangle given Area and Angle between Diagonal and Breadth Example

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

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

Here is how the Diagonal of Rectangle given Area and Angle between Diagonal and Breadth equation looks like.

10.1075 = \frac{\sqrt{48 \cdot \cot ((\frac{3.1416}{2}) - 55)}}{\cos ((\frac{3.1416}{2}) - 55)}

10.1075m = \frac{\sqrt{48m² \cdot \cot ((\frac{3.1416}{2}) - 55°)}}{\cos ((\frac{3.1416}{2}) - 55°)}

10.1075 = \frac{\sqrt{48 \cdot \cot ((\frac{3.1416}{2}) - 55)}}{\cos ((\frac{3.1416}{2}) - 55)}

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Diagonal of Rectangle given Area and Angle between Diagonal and Breadth Solution

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

FIRST Step Consider the formula

d = \frac{\sqrt{A \cdot \cot ((\frac{π}{2}) - ∠ db)}}{\cos ((\frac{π}{2}) - ∠ db)}

Next Step Substitute values of Variables

∴

d = \frac{\sqrt{48m² \cdot \cot ((\frac{π}{2}) - 55°)}}{\cos ((\frac{π}{2}) - 55°)}

Next Step Substitute values of Constants

∴

d = \frac{\sqrt{48m² \cdot \cot ((\frac{3.1416}{2}) - 55°)}}{\cos ((\frac{3.1416}{2}) - 55°)}

Next Step Convert Units

∴

d = \frac{\sqrt{48m² \cdot \cot ((\frac{3.1416}{2}) - 0.9599rad)}}{\cos ((\frac{3.1416}{2}) - 0.9599rad)}

Next Step Prepare to Evaluate

∴

d = \frac{\sqrt{48 \cdot \cot ((\frac{3.1416}{2}) - 0.9599)}}{\cos ((\frac{3.1416}{2}) - 0.9599)}

Next Step Evaluate

∴

d = 10.1074757559776m

LAST Step Rounding Answer

∴

d = 10.1075m

Diagonal of Rectangle given Area and Angle between Diagonal and Breadth 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

Area of Rectangle

Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Rectangle

Angle between Diagonal and Breadth of Rectangle

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

Symbol: ∠_db

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Angle between Diagonal and Breadth 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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

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 Area and Angle between Diagonal and Breadth?

Diagonal of Rectangle given Area and Angle between Diagonal and Breadth evaluator uses Diagonal of Rectangle = (sqrt(Area of Rectangle*cot((pi/2)-Angle between Diagonal and Breadth of Rectangle)))/(cos((pi/2)-Angle between Diagonal and Breadth of Rectangle)) to evaluate the Diagonal of Rectangle, The Diagonal of Rectangle given Area and Angle between Diagonal and Breadth formula is defined as the length of the line joining any pair of opposite vertices of the Rectangle and calculated using Area and Angle between Diagonal and Breadth of the Rectangle. Diagonal of Rectangle is denoted by d symbol.

How to evaluate Diagonal of Rectangle given Area and Angle between Diagonal and Breadth using this online evaluator? To use this online evaluator for Diagonal of Rectangle given Area and Angle between Diagonal and Breadth, enter Area of Rectangle (A) & Angle between Diagonal and Breadth of Rectangle (∠_db) and hit the calculate button.

FAQs on Diagonal of Rectangle given Area and Angle between Diagonal and Breadth

What is the formula to find Diagonal of Rectangle given Area and Angle between Diagonal and Breadth?

The formula of Diagonal of Rectangle given Area and Angle between Diagonal and Breadth is expressed as Diagonal of Rectangle = (sqrt(Area of Rectangle*cot((pi/2)-Angle between Diagonal and Breadth of Rectangle)))/(cos((pi/2)-Angle between Diagonal and Breadth of Rectangle)). Here is an example- 10.10748 = (sqrt(48*cot((pi/2)-0.959931088596701)))/(cos((pi/2)-0.959931088596701)).

How to calculate Diagonal of Rectangle given Area and Angle between Diagonal and Breadth?

With Area of Rectangle (A) & Angle between Diagonal and Breadth of Rectangle (∠_db) we can find Diagonal of Rectangle given Area and Angle between Diagonal and Breadth using the formula - Diagonal of Rectangle = (sqrt(Area of Rectangle*cot((pi/2)-Angle between Diagonal and Breadth of Rectangle)))/(cos((pi/2)-Angle between Diagonal and Breadth of Rectangle)). This formula also uses Archimedes' constant and , Cosine (cos), Cotangent (cot), 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 Area and Angle between Diagonal and Breadth be negative?

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

Which unit is used to measure Diagonal of Rectangle given Area and Angle between Diagonal and Breadth?

Diagonal of Rectangle given Area and Angle between Diagonal and Breadth 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 Area and Angle between Diagonal and Breadth can be measured.

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