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Diagonal of Rectangle given Area and Acute Angle between Diagonals 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{∠ d(Acute)}{2})}}{\cos (\frac{∠ d(Acute)}{2})}

d - Diagonal of Rectangle?A - Area of Rectangle?∠_d(Acute) - Acute Angle between Diagonals of Rectangle?

Diagonal of Rectangle given Area and Acute Angle between Diagonals Example

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

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

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

10.1075 = \frac{\sqrt{48 \cdot \cot (\frac{70}{2})}}{\cos (\frac{70}{2})}

10.1075m = \frac{\sqrt{48m² \cdot \cot (\frac{70°}{2})}}{\cos (\frac{70°}{2})}

10.1075 = \frac{\sqrt{48 \cdot \cot (\frac{70}{2})}}{\cos (\frac{70}{2})}

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Diagonal of Rectangle given Area and Acute Angle between Diagonals Solution

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

FIRST Step Consider the formula

d = \frac{\sqrt{A \cdot \cot (\frac{∠ d(Acute)}{2})}}{\cos (\frac{∠ d(Acute)}{2})}

Next Step Substitute values of Variables

∴

d = \frac{\sqrt{48m² \cdot \cot (\frac{70°}{2})}}{\cos (\frac{70°}{2})}

Next Step Convert Units

∴

d = \frac{\sqrt{48m² \cdot \cot (\frac{1.2217rad}{2})}}{\cos (\frac{1.2217rad}{2})}

Next Step Prepare to Evaluate

∴

d = \frac{\sqrt{48 \cdot \cot (\frac{1.2217}{2})}}{\cos (\frac{1.2217}{2})}

Next Step Evaluate

∴

d = 10.1074757559786m

LAST Step Rounding Answer

∴

d = 10.1075m

Diagonal of Rectangle given Area and Acute Angle between Diagonals 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

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

Acute Angle between Diagonals of Rectangle

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

Symbol: ∠_d(Acute)

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Acute Angle between Diagonals of Rectangle

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 Acute Angle between Diagonals?

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

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

FAQs on Diagonal of Rectangle given Area and Acute Angle between Diagonals

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

The formula of Diagonal of Rectangle given Area and Acute Angle between Diagonals is expressed as Diagonal of Rectangle = (sqrt(Area of Rectangle*cot(Acute Angle between Diagonals of Rectangle/2)))/(cos(Acute Angle between Diagonals of Rectangle/2)). Here is an example- 10.10748 = (sqrt(48*cot(1.2217304763958/2)))/(cos(1.2217304763958/2)).

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

With Area of Rectangle (A) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)) we can find Diagonal of Rectangle given Area and Acute Angle between Diagonals using the formula - Diagonal of Rectangle = (sqrt(Area of Rectangle*cot(Acute Angle between Diagonals of Rectangle/2)))/(cos(Acute Angle between Diagonals of Rectangle/2)). This formula also uses 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 Acute Angle between Diagonals be negative?

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

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

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

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