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Diagonal of Annulus Sector given outer circle radius and side length Solution

STEP 0: Pre-Calculation Summary
Formula Used
diagonal = sqrt(2*Outer radius*(1-cos(Theta))*(Outer radius-Side length)+Side length^2)
d = sqrt(2*router*(1-cos(ϑ))*(router-Lside)+Lside^2)
This formula uses 2 Functions, 3 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Outer radius - Outer radius of any figure is the radius of a larger circle of the two concentric circles that form its boundary. (Measured in Meter)
Theta - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint. (Measured in Degree)
Side length - Side length is the distance between the inner arc and the outer arc of Annulus Sector. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Outer radius: 10 Meter --> 10 Meter No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Side length: 5 Meter --> 5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = sqrt(2*router*(1-cos(ϑ))*(router-Lside)+Lside^2) --> sqrt(2*10*(1-cos(0.5235987755982))*(10-5)+5^2)
Evaluating ... ...
d = 6.19656837463738
STEP 3: Convert Result to Output's Unit
6.19656837463738 Meter --> No Conversion Required
FINAL ANSWER
6.19656837463738 Meter <-- Diagonal
(Calculation completed in 00.015 seconds)

10+ Annulus Sector Calculators

Diagonal of Annulus Sector
diagonal = sqrt(Outer radius^2+Inner radius^2-2*Outer radius*Inner radius*cos(Theta)) Go
Inner arc length of Annulus Sector given outer circle radius and side length
inner_arc_length = (2*(Outer radius-Side length)*pi*Theta)/(2*pi) Go
Outer arc length of Annuls Sector given inner circle radius and side length
outer_arc_length = (2*(Inner radius+Side length)*pi*Theta)/(2*pi) Go
Area of Annulus Sector
area = ((Outer radius^2-Inner radius^2)*pi*Theta)/(2*pi) Go
Inner arc length of Annulus Sector
inner_arc_length = (2*Inner radius*pi*Theta)/(2*pi) Go
Outer arc length of Annuls Sector
outer_arc_length = (2*Outer radius*pi*Theta)/(2*pi) Go
Perimeter of Annulus Sector
perimeter = Outer arc length+Inner arc length+(2*Side length) Go
Radius of outer circle of Annulus Sector
outer_radius = Inner radius+Side length Go
Radius of inner circle of Annulus Sector
inner_radius = Outer radius-Side length Go
Side length of Annulus Sector
side_length = Outer radius-Inner radius Go

Diagonal of Annulus Sector given outer circle radius and side length Formula

diagonal = sqrt(2*Outer radius*(1-cos(Theta))*(Outer radius-Side length)+Side length^2)
d = sqrt(2*router*(1-cos(ϑ))*(router-Lside)+Lside^2)

What is an Annulus Sector?

An Annulus Sector, also known as the circular ring sector, is a cut piece from an annulus that is joined by two straight lines from its center.

How to Calculate Diagonal of Annulus Sector given outer circle radius and side length?

Diagonal of Annulus Sector given outer circle radius and side length calculator uses diagonal = sqrt(2*Outer radius*(1-cos(Theta))*(Outer radius-Side length)+Side length^2) to calculate the Diagonal, The Diagonal of Annulus Sector given outer circle radius and side length formula is defined as the maximum distance between the two opposite points on the outer and inner arc. Diagonal is denoted by d symbol.

How to calculate Diagonal of Annulus Sector given outer circle radius and side length using this online calculator? To use this online calculator for Diagonal of Annulus Sector given outer circle radius and side length, enter Outer radius (router), Theta (ϑ) & Side length (Lside) and hit the calculate button. Here is how the Diagonal of Annulus Sector given outer circle radius and side length calculation can be explained with given input values -> 6.196568 = sqrt(2*10*(1-cos(0.5235987755982))*(10-5)+5^2).

FAQ

What is Diagonal of Annulus Sector given outer circle radius and side length?
The Diagonal of Annulus Sector given outer circle radius and side length formula is defined as the maximum distance between the two opposite points on the outer and inner arc and is represented as d = sqrt(2*router*(1-cos(ϑ))*(router-Lside)+Lside^2) or diagonal = sqrt(2*Outer radius*(1-cos(Theta))*(Outer radius-Side length)+Side length^2). Outer radius of any figure is the radius of a larger circle of the two concentric circles that form its boundary, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint & Side length is the distance between the inner arc and the outer arc of Annulus Sector.
How to calculate Diagonal of Annulus Sector given outer circle radius and side length?
The Diagonal of Annulus Sector given outer circle radius and side length formula is defined as the maximum distance between the two opposite points on the outer and inner arc is calculated using diagonal = sqrt(2*Outer radius*(1-cos(Theta))*(Outer radius-Side length)+Side length^2). To calculate Diagonal of Annulus Sector given outer circle radius and side length, you need Outer radius (router), Theta (ϑ) & Side length (Lside). With our tool, you need to enter the respective value for Outer radius, Theta & Side length 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 Diagonal?
In this formula, Diagonal uses Outer radius, Theta & Side length. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • outer_radius = Inner radius+Side length
  • outer_arc_length = (2*Outer radius*pi*Theta)/(2*pi)
  • inner_arc_length = (2*Inner radius*pi*Theta)/(2*pi)
  • diagonal = sqrt(Outer radius^2+Inner radius^2-2*Outer radius*Inner radius*cos(Theta))
  • perimeter = Outer arc length+Inner arc length+(2*Side length)
  • area = ((Outer radius^2-Inner radius^2)*pi*Theta)/(2*pi)
  • inner_radius = Outer radius-Side length
  • side_length = Outer radius-Inner radius
  • outer_arc_length = (2*(Inner radius+Side length)*pi*Theta)/(2*pi)
  • inner_arc_length = (2*(Outer radius-Side length)*pi*Theta)/(2*pi)
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