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.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
