Given two integers r and n where n is the number of sides of a regular polygon and r is the radius of the circle this polygon is circumscribed in. The task is to find the length of the side of polygon.
Examples:
Input: n = 5, r = 11
Output: 12.9256
Input: n = 3, r = 5
Output: 8.6576
Approach: Consider the image above and let angle AOB be theta then theta = 360 / n.
In right angled triangle 
, angle ACO = 90 degrees and angle AOC = theta / 2.
So, AC = OA * sin(theta / 2) = r * sin(theta / 2)
Therefore, side of the polygon, AB = 2 * AC i.e. 2 * r * sin(theta / 2).
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to calculate the side of the polygon// circumscribed in a circlefloat calculateSide(float n, float r){ float theta, theta_in_radians; theta = 360 / n; theta_in_radians = theta * 3.14 / 180; return 2 * r * sin(theta_in_radians / 2);}// Driver Codeint main(){ // Total sides of the polygon float n = 3; // Radius of the circumscribing circle float r = 5; cout << calculateSide(n, r);} |
Java
// Java implementation of the approachimport java.lang.Math;import java.io.*;class GFG { // Function to calculate the side of the polygon// circumscribed in a circlestatic double calculateSide(double n, double r){ double theta, theta_in_radians; theta = 360 / n; theta_in_radians = theta * 3.14 / 180; return 2 * r * Math.sin(theta_in_radians / 2);}// Driver Code public static void main (String[] args) { // Total sides of the polygon double n = 3; // Radius of the circumscribing circle double r = 5; System.out.println (calculateSide(n, r)); }//This code is contributed by akt_mit } |
Python3
# Python 3 implementation of the approachfrom math import sin# Function to calculate the side of # the polygon circumscribed in a circledef calculateSide(n, r): theta = 360 / n theta_in_radians = theta * 3.14 / 180 return 2 * r * sin(theta_in_radians / 2)# Driver Codeif __name__ == '__main__': # Total sides of the polygon n = 3 # Radius of the circumscribing circle r = 5 print('{0:.5}'.format(calculateSide(n, r)))# This code is contributed by# Sanjit_Prasad |
C#
// C# implementation of the approach using System;class GFG { // Function to calculate the side of the polygon // circumscribed in a circle static double calculateSide(double n, double r) { double theta, theta_in_radians; theta = 360 / n; theta_in_radians = theta * 3.14 / 180; return Math.Round(2 * r * Math.Sin(theta_in_radians / 2),4); } // Driver Code public static void Main () { // Total sides of the polygon double n = 3; // Radius of the circumscribing circle double r = 5; Console.WriteLine(calculateSide(n, r)); } // This code is contributed by Ryuga} |
PHP
<?php// PHP implementation of the approach// Function to calculate the side of the // polygon circumscribed in a circlefunction calculateSide($n, $r){ $theta; $theta_in_radians; $theta = 360 / $n; $theta_in_radians = $theta * 3.14 / 180; return 2 * $r * sin($theta_in_radians / 2);}// Driver Code// Total sides of the polygon$n = 3;// Radius of the circumscribing circle$r = 5;echo calculateSide($n, $r);// This code is contributed by inder_verma..?> |
Javascript
<script>// javascript implementation of the approach // Function to calculate the side of the polygon// circumscribed in a circlefunction calculateSide( n , r){ var theta, theta_in_radians; theta = 360 / n; theta_in_radians = theta * 3.14 / 180; return 2 * r * Math.sin(theta_in_radians / 2);}// Driver Code// Total sides of the polygonvar n = 3;// Radius of the circumscribing circlevar r = 5;document.write(calculateSide(n, r).toFixed(5));// This code contributed by Princi Singh </script> |
Output
8.6576
Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.
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