How to Calculate and Solve for Length of the Chord of a Small Circle | Latitude and Longitude
Last Updated on March 12, 2024
The image above represents length of the chord of a small circle. To calculate the length of the chord of a small circle, two essential parameters are needed and these parameters are Value of r and Angular Difference (θ).
The formula for calculating the length of the chord of a small circle:
l = 2rsin(θ / 2)
Where:
l = Length of the Chord of a Small Circle
r = Radius of the small circle
θ = Angular difference
Let’s solve an example;
Find the length of the chord of a small circle when the radius of the small circle is 6 and the angular difference is 14.
This implies that;
r = Radius of the Small Circle = 6
θ = Angular difference = 14
l = 2rsin(θ / 2)
l = 2(6)sin(14 / 2)
Then, l = (12)sin(7)
l = 12 x 0.1218
l = 1.46
Therefore, the length of the chord of the small circle is 1.46 km.
Calculating the Radius of the Small Circle when the Length of the Chord of the Small Circle and the Angular Difference are Given
r = l / 2sin(θ / 2)
Where;
r = Radius of the small circle
l = Length of the Chord of a Small Circle
θ = Angular difference
Let’s solve an example;
Find the radius of the small circle when the length of the chord of the small circle is 35 and the angular difference is 15.
This implies that;
l = Length of the Chord of a Small Circle = 35
θ = Angular difference = 15
r = l / 2sin(θ / 2)
r = 35 / 2sin(15 / 2)
So, r = 35 / 2sin(7.5)
r = 35 / 2 x 0.1305
That is, r = 35 / 0.261
r = 134.09
Therefore, the radius of the small circle is 134.09.
Read more: How to Calculate and Solve for Shortest Distance Between Two Points | Latitude and Longitude
Calculating the Angular Difference when the Length of the Chord of the Small Circle and the Radius of the Small Circle are Given
θ = 2sin-1 (l / 2r)
Where;
θ = Angular difference
l = Length of the Chord of a Small Circle
r = Radius of the small circle
Let’s solve an example;
Given that the length of the chord of the small circle is 25 and the radius of the small circle is 12. Find the angular difference.
This implies that;
l = Length of the Chord of a Small Circle = 25
r = Radius of the small circle = 12
θ = 2sin-1 (l / 2r)
That is, θ = 2sin-1 (25 / 2(12))
θ = 2sin-1 (25 / 24)
θ = 2sin-1 (1.04)
So, θ = 2 x 1.237
θ = 2.474
Therefore, the angular difference is 2.474°.
How to Calculate Length of the Chord of a Small Circle Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the length of the chord of a small circle.
To get the answer and workings of the length of the chord of a small circle 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 Length of the Chord of a Small Circle under Latitude and Longitude
The screenshot below displays the page or activity to enter your values, to get the answer for the length of the chord of a small circle according to the respective parameters which are the Value of r and Angular Difference (θ).
Now, enter the values appropriately and accordingly for the parameters as required by the Value of r is 6 and Angular Difference (θ) is 14.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the length of the chord of a small circle and presents the formula, workings and steps too.
