How to Calculate and Solve for Angle Subtended at the Centre by the Chord | Latitude and Longitude
Last Updated on March 12, 2024
The image above represents the angle subtended at the centre by the chord. To calculate the angle subtended by the centre at the chord, two essential parameters are needed and these parameters are Length of the Chord of the Small Circle (l) and Radius of the Earth (R).
The formula for calculating the angle subtended by the centre by the chord:
A(2β) = 2sin-1(l ⁄ 2R)
Where:
A(2β) = Angle Subtended at the Centre by the Chord
R = Radius of the Earth
l = Length of the Chord of a Small Circle
Let’s solve an example;
Find the angle subtended at the centre by the chord when the radius of the earth is 6 and the length of the chord of a small circle is 4.
This implies that;
R = Radius of the Earth = 6
l = Length of the Chord of a Small Circle = 4
A(2β) = 2sin-1(l ⁄ 2R)
A(2β) = 2sin-1(4 ⁄ 2 x 6)
So, A(2β) = 2sin-1(4 ⁄ 12)
A(2β) = 2sin-1(0.33)
Then, A(2β) = 2(19.47°)
A(2β) = 38.94
Therefore, the angle subtended at the centre by the chord is 38.94°.
Calculating the Radius of the Earth when the Angle Subtended at the Centre by the Chord and the Length of the Chord of a Small Circle are Given
R = L / 2sin(A(2B) / 2)
Where;
R = Radius of the Earth
A(2β) = Angle Subtended at the Centre by the Chord
l = Length of the Chord of a Small Circle
Let’s solve an example;
Find the radius of the earth when the angle subtended at the centre by the chord is 30 and the length of the chord of a small circle is 10.
This implies that;
A(2β) = Angle Subtended at the Centre by the Chord = 30
l = Length of the Chord of a Small Circle = 10
R = L / 2sin(A(2B) / 2)
R = 10 / 2sin(30 / 2)
So, R = 10 / 2sin(15)
R = 10 / 0.516
R = 19.37
Therefore, the radius of the earth is 19.37°.
Read more: How to Calculate and Solve for the Radius of a Small Circle | Latitude and Longitude
Calculating the Length of the Chord of a Small Circle when the Angle Subtended at the Centre by the Chord and the Radius of the Earth are Given
L = 2Rsin(A(2B) / 2)
Where;
l = Length of the Chord of a Small Circle
R = Radius of the Earth
A(2β) = Angle Subtended at the Centre by the Chord
Let’s solve an example;
Find the Length of the Chord of a small circle when the radius of the earth is 20 and the angle subtended at the centre by the chord is 40.
This implies that;
R = Radius of the Earth = 20
A(2β) = Angle Subtended at the Centre by the Chord = 40
L = 2Rsin(A(2B) / 2)
L = 2(20)sin(40 / 2)
Then, L = (40)sin(20)
L = (40) x 0.342
L = 13.68
Therefore, the length of the chord of a small circle is 13.68°.
How to Calculate the Angle Subtended at the Centre by the Chord Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the angle subtended at the centre by the chord.
To get the answer and workings of the angle subtended at the centre by the chord using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Latitude and Longitude under Mathematics.
Now, Click on Angle subtended at the Centre by the Chord under Latitude and Longitude
The screenshot below displays the page or activity to enter your values, to get the answer for the angle subtended at the centre by the chord according to the respective parameters which are the Length of the Chord of the Small Circle (l) and Radius of the Earth (R).
Now, enter the values appropriately and accordingly for the parameters as required by the Length of the Chord of the Small Circle (l) is 4 and the Radius of the Earth (R) is 6.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the angle subtended at the centre by the chord and presents the formula, workings and steps too.
