Acute Angle of Rhombus given Inradius Calculator

✖The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.ⓘ Inradius of Rhombus [r_i]			+10% -10%
✖The Side of Rhombus is the length of any of the four edges.ⓘ Side of Rhombus [S]			+10% -10%

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

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Acute Angle of Rhombus given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus)
∠_Acute = asin((2*r_i)/S)
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.
Inradius of Rhombus - (Measured in Meter) - The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus.
Side of Rhombus - (Measured in Meter) - The Side of Rhombus is the length of any of the four edges.

STEP 1: Convert Input(s) to Base Unit

Inradius of Rhombus: 3 Meter --> 3 Meter No Conversion Required
Side of Rhombus: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Acute = asin((2*r_i)/S) --> asin((2*3)/10)

Evaluating ... ...

∠_Acute = 0.643501108793284

STEP 3: Convert Result to Output's Unit

0.643501108793284 Radian -->36.869897645851 Degree (Check conversion here)

FINAL ANSWER

36.869897645851 ≈ 36.8699 Degree <-- Acute Angle of Rhombus

(Calculation completed in 00.020 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Acute Angle of Rhombus Calculators

Acute Angle of Rhombus given both Diagonals

LaTeX 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

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

Acute Angle of Rhombus given Long Diagonal

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

Acute Angle of Rhombus given Area

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

Acute Angle of Rhombus given Inradius Formula

LaTeX Go

Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus)
∠_Acute = asin((2*r_i)/S)

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 Inradius?

Acute Angle of Rhombus given Inradius calculator uses Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus) to calculate the Acute Angle of Rhombus, The Acute Angle of Rhombus given Inradius is defined as the angle inside the Rhombus which is less than 90 degrees, calculated using the inradius of the Rhombus. Acute Angle of Rhombus is denoted by ∠_Acute symbol.

How to calculate Acute Angle of Rhombus given Inradius using this online calculator? To use this online calculator for Acute Angle of Rhombus given Inradius, enter Inradius of Rhombus (r_i) & Side of Rhombus (S) and hit the calculate button. Here is how the Acute Angle of Rhombus given Inradius calculation can be explained with given input values -> 2112.49 = asin((2*3)/10).

FAQ

What is Acute Angle of Rhombus given Inradius?

The Acute Angle of Rhombus given Inradius is defined as the angle inside the Rhombus which is less than 90 degrees, calculated using the inradius of the Rhombus and is represented as ∠_Acute = asin((2*r_i)/S) or Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus). The Inradius of Rhombus is defined as the radius of the circle which is inscribed inside the Rhombus & The Side of Rhombus is the length of any of the four edges.

How to calculate Acute Angle of Rhombus given Inradius?

The Acute Angle of Rhombus given Inradius is defined as the angle inside the Rhombus which is less than 90 degrees, calculated using the inradius of the Rhombus is calculated using Acute Angle of Rhombus = asin((2*Inradius of Rhombus)/Side of Rhombus). To calculate Acute Angle of Rhombus given Inradius, you need Inradius of Rhombus (r_i) & Side of Rhombus (S). With our tool, you need to enter the respective value for Inradius of Rhombus & Side 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 Inradius of Rhombus & Side of Rhombus. We can use 3 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((2*Long Diagonal of Rhombus*Short Diagonal of Rhombus)/(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))

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