# Area of Triangle using Side-Angle-Side (length of two sides and the included angle)

Given two integers A, B representing the length of two sides of a triangle and an integer K representing the angle between them in radian, the task is to calculate the area of the triangle from the given information.

Examples:

Input: a = 9, b = 12, K = 2
Output: 49.1
Explanation:
Area of triangle = 1 / 2 * (9 * 12 * Sin 2) = 35.12

Input: A = 2, B = 4, K = 1
Output: 3.37

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:
Consider the following triangle ABC with sides A, B, C, and an angle K between sides A and B.

Then, the area of the triangle can be calculated using the Side-Angle-Side formula:

Below is the implementation of the above approach:

 // C++ program to calculate   // the area of a triangle when   // the length of two adjacent   // sides and the angle between   // them is provided   #include  using namespace std;     float Area_of_Triangle(int a, int b, int k)   {       float area = (float)((1 / 2.0) *                             a * b * (sin(k)));          return area;   }      // Driver Code   int main()  {       int a = 9;       int b = 12;       int k = 2;          // Function Call       float ans = Area_of_Triangle(a, b, k);          // Print the final answer       cout << ans << endl;  }      // This code is contributed by Ritik Bansal

 // Java program to calculate  // the area of a triangle when   // the length of two adjacent   // sides and the angle between  // them is provided  class GFG{     // Function to return the area of   // triangle using Side-Angle-Side  // formula   static float Area_of_Triangle(int a, int b,                                       int k)  {      float area = (float)((1 / 2.0) *                         a * b * Math.sin(k));         return area;  }     // Driver Code   public static void main(String[] args)  {      int a = 9;      int b = 12;      int k = 2;         // Function Call      float ans = Area_of_Triangle(a, b, k);         // Print the final answer      System.out.printf("%.1f",ans);  }  }     // This code is contributed by sapnasingh4991

 # Python3 program to calculate  # the area of a triangle when   # the length of two adjacent   # sides and the angle between  # them is provided     import math      # Function to return the area of   # triangle using Side-Angle-Side  # formula   def Area_of_Triangle(a, b, k):          area =(1 / 2) * a * b * math.sin(k)         return area      # Driver Code   a = 9 b = 12 k = 2    # Function Call   ans = Area_of_Triangle(a, b, k)      # Print the final answer   print(round(ans, 2))   

 // C# program to calculate  // the area of a triangle when   // the length of two adjacent   // sides and the angle between  // them is provided  using System;  class GFG{     // Function to return the area of   // triangle using Side-Angle-Side  // formula   static float Area_of_Triangle(int a, int b,                                       int k)  {      float area = (float)((1 / 2.0) *                     a * b * Math.Sin(k));         return area;  }     // Driver Code   public static void Main(String[] args)  {      int a = 9;      int b = 12;      int k = 2;         // Function Call      float ans = Area_of_Triangle(a, b, k);         // Print the readonly answer      Console.Write("{0:F1}", ans);  }  }     // This code is contributed by sapnasingh4991

Output:
49.1


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

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