# Length of diagonal of a parallelogram using adjacent sides and angle between them

Given two integers a and b where a and b represents the length of adjacent sides of a parallelogram and an angle 0 between them, the task is to find the length of diagonal of the parallelogram.

Examples:

Input: a = 6, b = 10, 0=30
Output: 6.14

Input: a = 3, b = 5, 0=45
Output: 3.58

Approach: Consider a parallelogram ABCD with sides a and b, now apply cosine rule at angle A in the triangle ABD to find the length of diagonal p, similarly find diagonal q from triangle ABC.

Therefore the diagonals is given by:

 // C++ program to find length  // Of diagonal of a parallelogram  // Using sides and angle between them.  #include  using namespace std;  #define PI 3.147     // Function to return the length  // Of diagonal of a parallelogram  // using sides and angle between them.  double Length_Diagonal(int a, int b, double theta)  {      double diagonal = sqrt((pow(a, 2) + pow(b, 2)) -                         2 * a * b * cos(theta * (PI / 180)));         return diagonal;  }     // Driver Code  int main()  {         // Given sides      int a = 3;      int b = 5;         // Given angle      double theta = 45;         // Function call      double ans = Length_Diagonal(a, b, theta);         // Print the final answer      printf("%.2f", ans);  }     // This code is contributed by Amit Katiyar

 // Java program to find length   // Of diagonal of a parallelogram   // Using sides and angle between them.  class GFG{     // Function to return the length  // Of diagonal of a parallelogram  // using sides and angle between them.  static double Length_Diagonal(int a, int b,                                double theta)  {      double diagonal = Math.sqrt((Math.pow(a, 2) +                                    Math.pow(b, 2)) -                                    2 * a * b *                                    Math.cos(theta *                                    (Math.PI / 180)));         return diagonal;  }     // Driver Code  public static void main(String[] args)  {             // Given sides      int a = 3;      int b = 5;         // Given angle      double theta = 45;         // Function call      double ans = Length_Diagonal(a, b, theta);         // Print the final answer      System.out.printf("%.2f", ans);  }  }     // This code is contributed by amal kumar choubey

 # Python3 Program to find length   # Of diagonal of a parallelogram   # Using sides and angle between them.     import math         # Function to return the length  # Of diagonal of a parallelogram   # using sides and angle between them.    def Length_Diagonal(a, b, theta):             diagonal = math.sqrt( ((a**2) + (b**2))      - 2 * a*b * math.cos(math.radians(theta)))             return diagonal         # Driver Code     # Given Sides  a = 3 b = 5    # Given Angle  theta = 45      # Function Call    ans = Length_Diagonal(a, b, theta)         # Print the final answer  print(round(ans, 2))

 // C# program to find length   // Of diagonal of a parallelogram   // Using sides and angle between them.  using System;     class GFG{     // Function to return the length  // Of diagonal of a parallelogram  // using sides and angle between them.  static double Length_Diagonal(int a, int b,                                double theta)  {      double diagonal = Math.Sqrt((Math.Pow(a, 2) +                                    Math.Pow(b, 2)) -                                    2 * a * b *                                    Math.Cos(theta *                                   (Math.PI / 180)));         return diagonal;  }     // Driver Code  public static void Main(String[] args)  {             // Given sides      int a = 3;      int b = 5;         // Given angle      double theta = 45;         // Function call      double ans = Length_Diagonal(a, b, theta);         // Print the readonly answer      Console.Write("{0:F2}", ans);  }  }     // This code is contributed by amal kumar choubey

Output:
3.58


Time Complexity: O(1)
Auxiliary Space: O(1)

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