Obtuse 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%

✖Obtuse Angle of Rhombus is the angle inside the Rhombus which is greater than 90 degree.ⓘ Obtuse Angle of Rhombus given Inradius [∠_Obtuse]

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Formula

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Obtuse Angle of Rhombus given Inradius

Formula

`"∠"_{"Obtuse"} = pi-asin((2*"r"_{"i"})/"S")`

Example

`"143.1301°"=pi-asin((2*"3m")/"10m")`

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Obtuse Angle of Rhombus given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Obtuse Angle of Rhombus = pi-asin((2*Inradius of Rhombus)/Side of Rhombus)
∠_Obtuse = pi-asin((2*r_i)/S)
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Obtuse Angle of Rhombus - (Measured in Radian) - Obtuse Angle of Rhombus is the angle inside the Rhombus which is greater 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

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

Evaluating ... ...

∠_Obtuse = 2.49809154479651

STEP 3: Convert Result to Output's Unit

2.49809154479651 Radian -->143.130102354183 Degree (Check conversion here)

FINAL ANSWER

143.130102354183 ≈ 143.1301 Degree <-- Obtuse Angle of Rhombus

(Calculation completed in 00.020 seconds)

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Created by Dhruv Walia

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

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< 6 Obtuse Angle of Rhombus Calculators

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))

Obtuse Angle of Rhombus given Inradius

Go Obtuse Angle of Rhombus = pi-asin((2*Inradius of Rhombus)/Side of Rhombus)

Obtuse Angle of Rhombus given Height

Go Obtuse Angle of Rhombus = pi-asin(Height of Rhombus/Side of Rhombus)

Obtuse Angle of Rhombus given Area

Go Obtuse Angle of Rhombus = pi-asin(Area of Rhombus/Side of Rhombus^2)

Obtuse Angle of Rhombus given Short Diagonal

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

Obtuse Angle of Rhombus given Long Diagonal

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

Obtuse Angle of Rhombus given Inradius Formula

Obtuse Angle of Rhombus = pi-asin((2*Inradius of Rhombus)/Side of Rhombus)
∠_Obtuse = pi-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 Obtuse Angle of Rhombus given Inradius?

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

How to calculate Obtuse Angle of Rhombus given Inradius using this online calculator? To use this online calculator for Obtuse Angle of Rhombus given Inradius, enter Inradius of Rhombus (r_i) & Side of Rhombus (S) and hit the calculate button. Here is how the Obtuse Angle of Rhombus given Inradius calculation can be explained with given input values -> 8200.751 = pi-asin((2*3)/10).

FAQ

What is Obtuse Angle of Rhombus given Inradius?

The Obtuse Angle of Rhombus given Inradius is defined as the angle inside the Rhombus which is greater than 90 degrees, calculated using inradius of the Rhombus and is represented as ∠_Obtuse = pi-asin((2*r_i)/S) or Obtuse Angle of Rhombus = pi-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 Obtuse Angle of Rhombus given Inradius?

The Obtuse Angle of Rhombus given Inradius is defined as the angle inside the Rhombus which is greater than 90 degrees, calculated using inradius of the Rhombus is calculated using Obtuse Angle of Rhombus = pi-asin((2*Inradius of Rhombus)/Side of Rhombus). To calculate Obtuse 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 Obtuse Angle of Rhombus?

In this formula, Obtuse Angle of Rhombus uses Inradius of Rhombus & Side of Rhombus. We can use 5 other way(s) to calculate the same, which is/are as follows -

Obtuse Angle of Rhombus = acos(Short Diagonal of Rhombus^2/(2*Side of Rhombus^2)-1)
Obtuse Angle of Rhombus = acos(1-Long Diagonal of Rhombus^2/(2*Side of Rhombus^2))
Obtuse Angle of Rhombus = 2*acos(Short Diagonal of Rhombus/sqrt(Long Diagonal of Rhombus^2+Short Diagonal of Rhombus^2))
Obtuse Angle of Rhombus = pi-asin(Area of Rhombus/Side of Rhombus^2)
Obtuse Angle of Rhombus = pi-asin(Height of Rhombus/Side of Rhombus)

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