Diagonal de un decágono regular

Dado un entero a que es el lado de un decágono regular, la tarea es encontrar e imprimir la longitud de su diagonal. 
 

Ejemplos: 
 

Entrada: a = 5 
Salida: 9.51
Entrada: a = 9 
Salida: 17.118 
 

Enfoque: Sabemos que la suma de los ángulos interiores de un polígono = (n – 2) * 180 donde, n es el no. de lados en el polígono. 
Entonces, la suma de los ángulos interiores del decágono = 8 * 180 = 1440 y cada ángulo interior será 144 . 
Ahora, tenemos que encontrar BC = 2 * x . Si dibujamos una perpendicular AO en BC , veremos que la perpendicular biseca a BC en BO y OC , ya que los triángulos AOB y AOC son congruentes entre sí. 
Entonces, en el triángulo AOB ,sin(72) = x / a ie x = 0.951 * a 
Por lo tanto, la longitud de la diagonal será 2 * x ie 1.902 * a .
A continuación se muestra la implementación del enfoque anterior: 
 

// C++ program to find the diagonal
// of a regular decagon
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the diagonal
// of a regular decagon
float decdiagonal(float a)
{
 
    // Side cannot be negative
    if (a < 0)
        return -1;
 
    // Length of the diagonal
    float d = 1.902 * a;
    return d;
}
 
// Driver code
int main()
{
    float a = 9;
    cout << decdiagonal(a) << endl;
    return 0;
}

// Java program to find the diagonal of a regular decdiagonal
import java.util.*;
import java.lang.*;
import java.io.*;
 
public class GFG {
 
    // Function to return the diagonal of a regular decdiagonal
    static double decdiagonal(double a)
    {
 
//side cannot be negative
        if(a<0)
        return -1;
 
        // length of the diagonal
        double d=1.902*a;
         
        return d;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int a = 9;
        System.out.println(decdiagonal(a));
    }
}

# Python3 program to find the diagonal
# of a regular decagon
 
# Function to return the diagonal
# of a regular decagon
def decdiagonal(a) :
 
    # Side cannot be negative
    if (a < 0) :
        return -1
 
    # Length of the diagonal
    d = 1.902 * a
    return d
 
# Driver code
if __name__ == "__main__" :
 
    a = 9
    print(decdiagonal(a))
     
# This code is contributed by Ryuga

// C# program to find the diagonal of a regular decdiagonal
using System;
 
public class GFG {
 
    // Function to return the diagonal of a regular decdiagonal
    static double decdiagonal(double a)
    {
 
//side cannot be negative
        if(a<0)
        return -1;
 
        // length of the diagonal
        double d=1.902*a;
         
        return d;
    }
 
    // Driver code
    public static void Main()
    {
        int a = 9;
        Console.WriteLine(decdiagonal(a));
    }
}
// This code is contributed by anuj_67..

<?php
// PHP program to find the diagonal
// of a regular decagon
 
// Function to return the diagonal
// of a regular decagon
function decdiagonal($a)
{
 
    // Side cannot be negative
    if ($a < 0)
        return -1;
 
    // Length of the diagonal
    $d = 1.902 * $a;
    return $d;
}
 
// Driver code
$a = 9;
echo decdiagonal($a);
 
// This code is contributed by ajit.
?>

<script>
// javascript program to find the diagonal of a regular decdiagonal
 
// Function to return the diagonal of a regular decdiagonal
function decdiagonal(a)
{
 
// side cannot be negative
if(a < 0)
return -1;
 
// length of the diagonal
var d = 1.902*a;
 
return d;
}
 
// Driver code
 
var a = 9;
document.write(decdiagonal(a));
 
// This code contributed by Princi Singh
</script>

17.118

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)