Acute Angle of Rhombus given both Diagonals Calculator

✖The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.ⓘ Long Diagonal of Rhombus [d_Long]			+10% -10%
✖A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus.ⓘ Short Diagonal of Rhombus [d_Short]			+10% -10%

✖Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.ⓘ Acute Angle of Rhombus given both Diagonals [∠_Acute]

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Formula

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Acute Angle of Rhombus given both Diagonals

Formula

`"∠"_{"Acute"} = asin((2*"d"_{"Long"}*"d"_{"Short"})/("d"_{"Long"}^2+"d"_{"Short"}^2))`

Example

`"47.92498°"=asin((2*"18m"*"8m")/(("18m")^2+("8m")^2))`

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Acute Angle of Rhombus given both Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acute Angle of Rhombus = asin((2*Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))
∠_Acute = asin((2*d_Long*d_Short)/(d_Long^2+d_Short^2))
This formula uses 2 Functions, 3 Variables

Functions Used

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., sin(Angle)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

Acute Angle of Rhombus - (Measured in Radian) - Acute Angle of Rhombus is the angle inside the Rhombus which is less than 90 degree.
Long Diagonal of Rhombus - (Measured in Meter) - The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus.
Short Diagonal of Rhombus - (Measured in Meter) - A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus.

STEP 1: Convert Input(s) to Base Unit

Long Diagonal of Rhombus: 18 Meter --> 18 Meter No Conversion Required
Short Diagonal of Rhombus: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Acute = asin((2*d_Long*d_Short)/(d_Long^2+d_Short^2)) --> asin((2*18*8)/(18^2+8^2))

Evaluating ... ...

∠_Acute = 0.836448659158458

STEP 3: Convert Result to Output's Unit

0.836448659158458 Radian -->47.9249779491654 Degree (Check conversion here)

FINAL ANSWER

47.9249779491654 ≈ 47.92498 Degree <-- Acute Angle of Rhombus

(Calculation completed in 00.004 seconds)

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< 6 Acute Angle of Rhombus Calculators

Acute Angle of Rhombus given both Diagonals

Go Acute Angle of Rhombus = asin((2*Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))

Acute Angle of Rhombus given Short Diagonal

Go Acute Angle of Rhombus = acos(1-Short Diagonal of Rhombus^2/(2*Side of Rhombus^2))

Acute Angle of Rhombus given Long Diagonal

Go Acute Angle of Rhombus = acos(Long Diagonal of Rhombus^2/(2*Side of Rhombus^2)-1)

Acute Angle of Rhombus given Inradius

Go Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus)

Acute Angle of Rhombus given Height

Go Acute Angle of Rhombus = asin(Height of Rhombus/Side of Rhombus)

Acute Angle of Rhombus given Area

Go Acute Angle of Rhombus = asin(Area of Rhombus/Side of Rhombus^2)

< 4 Angles of Rhombus Calculators

Acute Angle of Rhombus given both Diagonals

Go Acute Angle of Rhombus = asin((2*Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))

Obtuse Angle of Rhombus given both Diagonals

Go Obtuse Angle of Rhombus = 2*acos(Short Diagonal of Rhombus/sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))

Acute Angle of Rhombus given Short Diagonal

Go Acute Angle of Rhombus = acos(1-Short Diagonal of Rhombus^2/(2*Side of Rhombus^2))

Acute Angle of Rhombus given Long Diagonal

Go Acute Angle of Rhombus = acos(Long Diagonal of Rhombus^2/(2*Side of Rhombus^2)-1)

Acute Angle of Rhombus given both Diagonals Formula

What is Rhombus?

A Rhombus is a special case of a parallelogram. In a Rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a Rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or Rhombus diamond. The plural form of a Rhombus is Rhombi or Rhombuses.

How to Calculate Acute Angle of Rhombus given both Diagonals?

Acute Angle of Rhombus given both Diagonals calculator uses Acute Angle of Rhombus = asin((2*Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2)) to calculate the Acute Angle of Rhombus, Acute Angle of Rhombus given both Diagonals is defined as the angle inside the Rhombus which is less than 90 degrees, calculated using both diagonals of the Rhombus. Acute Angle of Rhombus is denoted by ∠_Acute symbol.

How to calculate Acute Angle of Rhombus given both Diagonals using this online calculator? To use this online calculator for Acute Angle of Rhombus given both Diagonals, enter Long Diagonal of Rhombus (d_Long) & Short Diagonal of Rhombus (d_Short) and hit the calculate button. Here is how the Acute Angle of Rhombus given both Diagonals calculation can be explained with given input values -> 2745.899 = asin((2*18*8)/(18^2+8^2)).

FAQ

What is Acute Angle of Rhombus given both Diagonals?

Acute Angle of Rhombus given both Diagonals is defined as the angle inside the Rhombus which is less than 90 degrees, calculated using both diagonals of the Rhombus and is represented as ∠_Acute = asin((2*d_Long*d_Short)/(d_Long^2+d_Short^2)) or Acute Angle of Rhombus = asin((2*Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2)). The Long Diagonal of Rhombus is the length of line joining the acute angle corners of a Rhombus & A Short Diagonal of Rhombus is a length of the line joining the obtuse angle corners of a Rhombus.

How to calculate Acute Angle of Rhombus given both Diagonals?

Acute Angle of Rhombus given both Diagonals is defined as the angle inside the Rhombus which is less than 90 degrees, calculated using both diagonals of the Rhombus is calculated using Acute Angle of Rhombus = asin((2*Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2)). To calculate Acute Angle of Rhombus given both Diagonals, you need Long Diagonal of Rhombus (d_Long) & Short Diagonal of Rhombus (d_Short). With our tool, you need to enter the respective value for Long Diagonal of Rhombus & Short Diagonal of Rhombus and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Acute Angle of Rhombus?

In this formula, Acute Angle of Rhombus uses Long Diagonal of Rhombus & Short Diagonal of Rhombus. We can use 7 other way(s) to calculate the same, which is/are as follows -

Acute Angle of Rhombus = acos(Long Diagonal of Rhombus^2/(2*Side of Rhombus^2)-1)
Acute Angle of Rhombus = acos(1-Short Diagonal of Rhombus^2/(2*Side of Rhombus^2))
Acute Angle of Rhombus = asin(Area of Rhombus/Side of Rhombus^2)
Acute Angle of Rhombus = asin(Height of Rhombus/Side of Rhombus)
Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus)
Acute Angle of Rhombus = acos(Long Diagonal of Rhombus^2/(2*Side of Rhombus^2)-1)
Acute Angle of Rhombus = acos(1-Short Diagonal of Rhombus^2/(2*Side of Rhombus^2))

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