{"id":2471,"date":"2019-11-20T16:55:27","date_gmt":"2019-11-20T15:55:27","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=2471"},"modified":"2024-03-12T17:06:28","modified_gmt":"2024-03-12T16:06:28","slug":"how-to-calculate-and-solve-for-angle-subtended-at-the-centre-by-the-chord-latitude-and-longitude","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2019\/11\/20\/how-to-calculate-and-solve-for-angle-subtended-at-the-centre-by-the-chord-latitude-and-longitude\/","title":{"rendered":"How to Calculate and Solve for Angle Subtended at the Centre by the Chord | Latitude and Longitude"},"content":{"rendered":"

\"\"<\/p>\n

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)<\/strong> and Radius of the Earth (R).<\/strong><\/p>\n

The formula for calculating the angle subtended by the centre by the chord:<\/p>\n

A(2\u03b2) = 2sin-1<\/sup>(l<\/sup> \u2044 2R<\/sub>)<\/p>\n

Where:<\/p>\n

A(2\u03b2) = Angle Subtended at the Centre by the Chord
\nR = Radius of the Earth
\nl = Length of the Chord of a Small Circle<\/p>\n

Let’s solve an example;
\nFind 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.<\/p>\n

This implies that;<\/p>\n

R = Radius of the Earth = 6
\nl = Length of the Chord of a Small Circle = 4<\/p>\n

A(2\u03b2) = 2sin-1<\/sup>(l<\/sup> \u2044 2R<\/sub>)
\nA(2\u03b2) = 2sin-1<\/sup>(4<\/sup> \u2044 2 x 6<\/sub>)
\nSo, A(2\u03b2) = 2sin-1<\/sup>(4<\/sup> \u2044 12<\/sub>)
\nA(2\u03b2) = 2sin-1<\/sup>(0.33)
\nThen, A(2\u03b2) = 2(19.47\u00b0<\/strong>)
\nA(2\u03b2) = 38.94<\/p>\n

Therefore, the\u00a0angle subtended at the centre by the chord\u00a0<\/strong>is\u00a038.94\u00b0.<\/strong><\/p>\n

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<\/strong><\/h3>\n

R = L<\/sup> \/ 2sin(A(2B)<\/sup> \/ 2<\/sub>)<\/sub><\/p>\n

Where;<\/p>\n

R = Radius of the Earth
\nA(2\u03b2) = Angle Subtended at the Centre by the Chord
\nl = Length of the Chord of a Small Circle<\/p>\n

Let’s solve an example;
\nFind 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.<\/p>\n

This implies that;<\/p>\n

A(2\u03b2) = Angle Subtended at the Centre by the Chord = 30
\nl = Length of the Chord of a Small Circle = 10<\/p>\n

R = L<\/sup> \/ 2sin(A(2B)<\/sup> \/ 2<\/sub>)<\/sub>
\nR = 10<\/sup> \/ 2sin(30<\/sup> \/ 2<\/sub>)<\/sub>
\nSo, R = 10<\/sup> \/ 2sin(15)<\/sub>
\nR = 10<\/sup> \/ 0.516<\/sub>
\nR = 19.37<\/p>\n

Therefore, the\u00a0radius of the earth\u00a0<\/strong>is 19.37\u00b0.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for the Radius of a Small Circle | Latitude and Longitude<\/a><\/p>\n

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<\/strong><\/h3>\n

L = 2Rsin(A(2B)<\/sup> \/ 2<\/sub>)<\/p>\n

Where;<\/p>\n

l = Length of the Chord of a Small Circle
\nR = Radius of the Earth
\nA(2\u03b2) = Angle Subtended at the Centre by the Chord<\/p>\n

Let’s solve an example;
\nFind 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.<\/p>\n

This implies that;<\/p>\n

R = Radius of the Earth = 20
\nA(2\u03b2) = Angle Subtended at the Centre by the Chord = 40<\/p>\n

L = 2Rsin(A(2B)<\/sup> \/ 2<\/sub>)
\nL = 2(20)sin(40<\/sup> \/ 2<\/sub>)
\nThen, L = (40)sin(20)
\nL = (40) x 0.342
\nL = 13.68<\/p>\n

Therefore, the\u00a0length of the chord of a small circle\u00a0<\/strong>is\u00a013.68\u00b0.<\/strong><\/p>\n

How to Calculate the Angle Subtended at the Centre by the Chord Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the angle subtended at the centre by the chord.<\/p>\n

To get the answer and workings of the angle subtended at the centre by the chord using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>for\u00a0NGN 1,500\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a>
\nApple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on Latitude and Longitude<\/strong>\u00a0<\/strong>under Mathematics<\/strong>.<\/p>\n

\"\"<\/p>\n

Now, Click on Angle subtended at the Centre by the Chord<\/strong>\u00a0<\/strong>under\u00a0Latitude and Longitude<\/strong><\/p>\n

\"\"<\/p>\n

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)<\/strong> and Radius of the Earth (R).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Length of the Chord of the Small Circle (l)<\/strong> is 4 <\/strong>and the Radius of the Earth (R)<\/strong> is 6<\/strong>.<\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/p>\n

\"\"
\n\"How<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the angle subtended at the centre by the chord and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents the angle subtended at the centre by the chord. To calculate the angle subtended…","protected":false},"author":5,"featured_media":13302,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Calculate Angle Subtended at the Centre by the Chord","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn the steps and formula on How to Calculate and Solve for Angle Subtended at the Centre by the Chord | Latitude and 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