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Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals Formula

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GoPerimeter of Rectangle given Diagonal and Length Formula

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

P = 4 \cdot r c \cdot \sqrt{1 + (2 \cdot \sin (\frac{∠ d(Acute)}{2}) \cdot \cos (\frac{∠ d(Acute)}{2}))}

P - Perimeter of Rectangle?r_c - Circumradius of Rectangle?∠_d(Acute) - Acute Angle between Diagonals of Rectangle?

Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals Example

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

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

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

27.8546 = 4 \cdot 5 \cdot \sqrt{1 + (2 \cdot \sin (\frac{70}{2}) \cdot \cos (\frac{70}{2}))}

27.8546m = 4 \cdot 5m \cdot \sqrt{1 + (2 \cdot \sin (\frac{70°}{2}) \cdot \cos (\frac{70°}{2}))}

27.8546 = 4 \cdot 5 \cdot \sqrt{1 + (2 \cdot \sin (\frac{70}{2}) \cdot \cos (\frac{70}{2}))}

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Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals Solution

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

FIRST Step Consider the formula

P = 4 \cdot r c \cdot \sqrt{1 + (2 \cdot \sin (\frac{∠ d(Acute)}{2}) \cdot \cos (\frac{∠ d(Acute)}{2}))}

Next Step Substitute values of Variables

∴

P = 4 \cdot 5m \cdot \sqrt{1 + (2 \cdot \sin (\frac{70°}{2}) \cdot \cos (\frac{70°}{2}))}

Next Step Convert Units

∴

P = 4 \cdot 5m \cdot \sqrt{1 + (2 \cdot \sin (\frac{1.2217rad}{2}) \cdot \cos (\frac{1.2217rad}{2}))}

Next Step Prepare to Evaluate

∴

P = 4 \cdot 5 \cdot \sqrt{1 + (2 \cdot \sin (\frac{1.2217}{2}) \cdot \cos (\frac{1.2217}{2}))}

Next Step Evaluate

∴

P = 27.8545696128002m

LAST Step Rounding Answer

∴

P = 27.8546m

Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals Formula Elements

Variables

Functions

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

Circumradius of Rectangle

Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius 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

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)

cos

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

Syntax: cos(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 Perimeter of Rectangle

Go Perimeter of Rectangle

P = 2 \cdot (l + b)

Go Perimeter of Rectangle given Diagonal and Length

P = 2 \cdot (l + \sqrt{d^{2} - l^{2}})

Go Perimeter of Rectangle given Area and Length

P = \frac{2 \cdot (A + l^{2})}{l}

Go Perimeter of Rectangle given Breadth and Circumradius

P = 2 \cdot (b + \sqrt{(4 \cdot {r c}^{2}) - b^{2}})

How to Evaluate Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals?

Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals evaluator uses Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2))) to evaluate the Perimeter of Rectangle, The Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals formula is defined as the total length of all the boundary lines of the Rectangle, and calculated using Circumradius and Acute Angle between Diagonals of the Rectangle. Perimeter of Rectangle is denoted by P symbol.

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

FAQs on Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals

What is the formula to find Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals?

The formula of Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals is expressed as Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2))). Here is an example- 27.85457 = 4*5*sqrt(1+(2*sin(1.2217304763958/2)*cos(1.2217304763958/2))).

How to calculate Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals?

With Circumradius of Rectangle (r_c) & Acute Angle between Diagonals of Rectangle (∠_d(Acute)) we can find Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals using the formula - Perimeter of Rectangle = 4*Circumradius of Rectangle*sqrt(1+(2*sin(Acute Angle between Diagonals of Rectangle/2)*cos(Acute Angle between Diagonals of Rectangle/2))). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Perimeter of Rectangle?

Here are the different ways to Calculate Perimeter of Rectangle-

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

Can the Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals be negative?

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

Which unit is used to measure Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals?

Perimeter of Rectangle given Circumradius 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 Perimeter of Rectangle given Circumradius and Acute Angle between Diagonals can be measured.

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